<?xml version='1.0' encoding='utf-8'?>
<FilingSummary>
  <Version>3.24.1.1.u2</Version>
  <ProcessingTime/>
  <ReportFormat>html</ReportFormat>
  <ContextCount>94</ContextCount>
  <ElementCount>218</ElementCount>
  <EntityCount>1</EntityCount>
  <FootnotesReported>false</FootnotesReported>
  <SegmentCount>38</SegmentCount>
  <ScenarioCount>0</ScenarioCount>
  <TuplesReported>false</TuplesReported>
  <UnitCount>5</UnitCount>
  <MyReports>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R1.htm</HtmlFileName>
      <LongName>100000 - Document - Document and Entity Information</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DocumentDocumentAndEntityInformation</Role>
      <ShortName>Document and Entity Information</ShortName>
      <MenuCategory>Cover</MenuCategory>
      <Position>1</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R2.htm</HtmlFileName>
      <LongName>100010 - Statement - Condensed Consolidated Balance Sheets (Unaudited)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/StatementCondensedConsolidatedBalanceSheetsUnaudited</Role>
      <ShortName>Condensed Consolidated Balance Sheets (Unaudited)</ShortName>
      <MenuCategory>Statements</MenuCategory>
      <Position>2</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R3.htm</HtmlFileName>
      <LongName>100030 - Statement - Condensed Consolidated Balance Sheets (Parenthetical)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/StatementCondensedConsolidatedBalanceSheetsParenthetical</Role>
      <ShortName>Condensed Consolidated Balance Sheets (Parenthetical)</ShortName>
      <MenuCategory>Statements</MenuCategory>
      <Position>3</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R4.htm</HtmlFileName>
      <LongName>100040 - Statement - Condensed Consolidated Statements of Operations and Comprehensive Loss (Unaudited)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/StatementCondensedConsolidatedStatementsOfOperationsAndComprehensiveLossUnaudited</Role>
      <ShortName>Condensed Consolidated Statements of Operations and Comprehensive Loss (Unaudited)</ShortName>
      <MenuCategory>Statements</MenuCategory>
      <Position>4</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R5.htm</HtmlFileName>
      <LongName>100050 - Statement - Condensed Consolidated Statements of Equity (Deficit)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/StatementCondensedConsolidatedStatementsOfEquityDeficit</Role>
      <ShortName>Condensed Consolidated Statements of Equity (Deficit)</ShortName>
      <MenuCategory>Statements</MenuCategory>
      <Position>5</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R6.htm</HtmlFileName>
      <LongName>100060 - Statement - Condensed Consolidated Statements of Cash Flows</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/StatementCondensedConsolidatedStatementsOfCashFlows</Role>
      <ShortName>Condensed Consolidated Statements of Cash Flows</ShortName>
      <MenuCategory>Statements</MenuCategory>
      <Position>6</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R7.htm</HtmlFileName>
      <LongName>995410 - Disclosure - Pay vs Performance Disclosure</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://xbrl.sec.gov/ecd/role/PvpDisclosure</Role>
      <ShortName>Pay vs Performance Disclosure</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>7</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R8.htm</HtmlFileName>
      <LongName>995445 - Disclosure - Insider Trading Arrangements</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://xbrl.sec.gov/ecd/role/InsiderTradingArrangements</Role>
      <ShortName>Insider Trading Arrangements</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>8</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R9.htm</HtmlFileName>
      <LongName>995455 - Disclosure - Organization and Description of Business</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureOrganizationAndDescriptionOfBusiness</Role>
      <ShortName>Organization and Description of Business</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>9</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R10.htm</HtmlFileName>
      <LongName>995465 - Disclosure - Basis of Presentation and Summary of Significant Accounting Policies</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureBasisOfPresentationAndSummaryOfSignificantAccountingPolicies</Role>
      <ShortName>Basis of Presentation and Summary of Significant Accounting Policies</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>10</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R11.htm</HtmlFileName>
      <LongName>995475 - Disclosure - Cash, Cash Equivalents and Marketable Securities</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureCashCashEquivalentsAndMarketableSecurities</Role>
      <ShortName>Cash, Cash Equivalents and Marketable Securities</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>11</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R12.htm</HtmlFileName>
      <LongName>995485 - Disclosure - Fair Value</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureFairValue</Role>
      <ShortName>Fair Value</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>12</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R13.htm</HtmlFileName>
      <LongName>995495 - Disclosure - Property and Equipment, Net</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosurePropertyAndEquipmentNet</Role>
      <ShortName>Property and Equipment, Net</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>13</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R14.htm</HtmlFileName>
      <LongName>995505 - Disclosure - Accrued Expenses</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureAccruedExpenses</Role>
      <ShortName>Accrued Expenses</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>14</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R15.htm</HtmlFileName>
      <LongName>995515 - Disclosure - Leases</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureLeases</Role>
      <ShortName>Leases</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>15</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R16.htm</HtmlFileName>
      <LongName>995525 - Disclosure - Share-Based Compensation</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureSharebasedCompensation</Role>
      <ShortName>Share-Based Compensation</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>16</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R17.htm</HtmlFileName>
      <LongName>995535 - Disclosure - Income Taxes</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureIncomeTaxes</Role>
      <ShortName>Income Taxes</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>17</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R18.htm</HtmlFileName>
      <LongName>995545 - Disclosure - Commitments and Contingencies</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureCommitmentsAndContingencies</Role>
      <ShortName>Commitments and Contingencies</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>18</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R19.htm</HtmlFileName>
      <LongName>995555 - Disclosure - Related Parties</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureRelatedParties</Role>
      <ShortName>Related Parties</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>19</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R20.htm</HtmlFileName>
      <LongName>995575 - Disclosure - Earnings Per Share</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureEarningsPerShare1</Role>
      <ShortName>Earnings Per Share</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>20</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R21.htm</HtmlFileName>
      <LongName>995595 - Disclosure - Basis of Presentation and Summary of Significant Accounting Policies (Policies)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureBasisOfPresentationAndSummaryOfSignificantAccountingPoliciesPolicies</Role>
      <ShortName>Basis of Presentation and Summary of Significant Accounting Policies (Policies)</ShortName>
      <MenuCategory>Policies</MenuCategory>
      <ParentRole>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureBasisOfPresentationAndSummaryOfSignificantAccountingPolicies</ParentRole>
      <Position>21</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R22.htm</HtmlFileName>
      <LongName>995605 - Disclosure - Cash, Cash Equivalents and Marketable Securities (Tables)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureCashCashEquivalentsAndMarketableSecuritiesTables</Role>
      <ShortName>Cash, Cash Equivalents and Marketable Securities (Tables)</ShortName>
      <MenuCategory>Tables</MenuCategory>
      <ParentRole>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureCashCashEquivalentsAndMarketableSecurities</ParentRole>
      <Position>22</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R23.htm</HtmlFileName>
      <LongName>995615 - Disclosure - Fair Value (Tables)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureFairValueTables</Role>
      <ShortName>Fair Value (Tables)</ShortName>
      <MenuCategory>Tables</MenuCategory>
      <ParentRole>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureFairValue</ParentRole>
      <Position>23</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R24.htm</HtmlFileName>
      <LongName>995625 - Disclosure - Property and Equipment, Net (Tables)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosurePropertyAndEquipmentNetTables</Role>
      <ShortName>Property and Equipment, Net (Tables)</ShortName>
      <MenuCategory>Tables</MenuCategory>
      <ParentRole>http://www.muraloncology.com/20240331/taxonomy/role/DisclosurePropertyAndEquipmentNet</ParentRole>
      <Position>24</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R25.htm</HtmlFileName>
      <LongName>995635 - Disclosure - Accrued Expenses (Tables)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureAccruedExpensesTables</Role>
      <ShortName>Accrued Expenses (Tables)</ShortName>
      <MenuCategory>Tables</MenuCategory>
      <ParentRole>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureAccruedExpenses</ParentRole>
      <Position>25</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R26.htm</HtmlFileName>
      <LongName>995645 - Disclosure - Net Loss per Share (Tables)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureNetLossPerShareTables</Role>
      <ShortName>Net Loss per Share (Tables)</ShortName>
      <MenuCategory>Tables</MenuCategory>
      <Position>26</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R27.htm</HtmlFileName>
      <LongName>995655 - Disclosure - Leases (Tables)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureLeasesTables</Role>
      <ShortName>Leases (Tables)</ShortName>
      <MenuCategory>Tables</MenuCategory>
      <ParentRole>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureLeases</ParentRole>
      <Position>27</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R28.htm</HtmlFileName>
      <LongName>995665 - Disclosure - Share-Based Compensation (Tables)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureSharebasedCompensationTables</Role>
      <ShortName>Share-Based Compensation (Tables)</ShortName>
      <MenuCategory>Tables</MenuCategory>
      <ParentRole>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureSharebasedCompensation</ParentRole>
      <Position>28</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R29.htm</HtmlFileName>
      <LongName>995675 - Disclosure - Organization and Description of Business - Additional Information (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureOrganizationAndDescriptionOfBusinessAdditionalInformationDetails</Role>
      <ShortName>Organization and Description of Business - Additional Information (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>29</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R30.htm</HtmlFileName>
      <LongName>995685 - Disclosure - Cash, Cash Equivalents and Marketable Securities - Additional Information (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureCashCashEquivalentsAndMarketableSecuritiesAdditionalInformationDetails</Role>
      <ShortName>Cash, Cash Equivalents and Marketable Securities - Additional Information (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>30</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R31.htm</HtmlFileName>
      <LongName>995695 - Disclosure - Cash, Cash Equivalents and Marketable Securities - Schedule of Marketable Securities (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureCashCashEquivalentsAndMarketableSecuritiesScheduleOfMarketableSecuritiesDetails</Role>
      <ShortName>Cash, Cash Equivalents and Marketable Securities - Schedule of Marketable Securities (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>31</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R32.htm</HtmlFileName>
      <LongName>995705 - Disclosure - Cash, Cash Equivalents and Marketable Securities - Schedule of Marketable Securities in Continuous Unrealized Loss Position (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureCashCashEquivalentsAndMarketableSecuritiesScheduleOfMarketableSecuritiesInContinuousUnrealizedLossPositionDetails</Role>
      <ShortName>Cash, Cash Equivalents and Marketable Securities - Schedule of Marketable Securities in Continuous Unrealized Loss Position (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>32</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R33.htm</HtmlFileName>
      <LongName>995715 - Disclosure - Fair Value - Financial Assets Measured and Recognized at Fair Value on Recurring Basis (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureFairValueFinancialAssetsMeasuredAndRecognizedAtFairValueOnRecurringBasisDetails</Role>
      <ShortName>Fair Value - Financial Assets Measured and Recognized at Fair Value on Recurring Basis (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>33</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R34.htm</HtmlFileName>
      <LongName>995725 - Disclosure - Property and Equipment, Net - Schedule of Property and Equipment, Net (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosurePropertyAndEquipmentNetScheduleOfPropertyAndEquipmentNetDetails</Role>
      <ShortName>Property and Equipment, Net - Schedule of Property and Equipment, Net (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>34</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R35.htm</HtmlFileName>
      <LongName>995735 - Disclosure - Property and Equipment, Net - Additional Information (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosurePropertyAndEquipmentNetAdditionalInformationDetails</Role>
      <ShortName>Property and Equipment, Net - Additional Information (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>35</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R36.htm</HtmlFileName>
      <LongName>995745 - Disclosure - Accrued Expenses - Components of Accrued Expenses (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureAccruedExpensesComponentsOfAccruedExpensesDetails</Role>
      <ShortName>Accrued Expenses - Components of Accrued Expenses (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>36</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R37.htm</HtmlFileName>
      <LongName>995755 - Disclosure - Leases - Additional Information (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureLeasesAdditionalInformationDetails</Role>
      <ShortName>Leases - Additional Information (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>37</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R38.htm</HtmlFileName>
      <LongName>995765 - Disclosure - Leases - Summary of Effect of Lease Costs in Unaudited Condensed Combined Statements of Operations (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureLeasesSummaryOfEffectOfLeaseCostsInUnauditedCondensedCombinedStatementsOfOperationsDetails</Role>
      <ShortName>Leases - Summary of Effect of Lease Costs in Unaudited Condensed Combined Statements of Operations (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>38</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R39.htm</HtmlFileName>
      <LongName>995775 - Disclosure - Leases - Schedule of Future Lease Payments under Non-cancelable Leases (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureLeasesScheduleOfFutureLeasePaymentsUnderNoncancelableLeasesDetails</Role>
      <ShortName>Leases - Schedule of Future Lease Payments under Non-cancelable Leases (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>39</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R40.htm</HtmlFileName>
      <LongName>995785 - Disclosure - Share-Based Compensation - Summary of Assumption Estimate Fair Value of Stock Options Granted (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureSharebasedCompensationSummaryOfAssumptionEstimateFairValueOfStockOptionsGrantedDetails</Role>
      <ShortName>Share-Based Compensation - Summary of Assumption Estimate Fair Value of Stock Options Granted (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>40</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R41.htm</HtmlFileName>
      <LongName>995795 - Disclosure - Share-Based Compensation - Summary of Stock Option Activity (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureSharebasedCompensationSummaryOfStockOptionActivityDetails</Role>
      <ShortName>Share-Based Compensation - Summary of Stock Option Activity (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>41</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R42.htm</HtmlFileName>
      <LongName>995805 - Disclosure - Share-Based Compensation - Summary of Restricted Share Activity (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureSharebasedCompensationSummaryOfRestrictedShareActivityDetails</Role>
      <ShortName>Share-Based Compensation - Summary of Restricted Share Activity (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>42</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R43.htm</HtmlFileName>
      <LongName>995815 - Disclosure - Share-Based Compensation - Additional Information (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureSharebasedCompensationAdditionalInformationDetails</Role>
      <ShortName>Share-Based Compensation - Additional Information (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>43</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R44.htm</HtmlFileName>
      <LongName>995825 - Disclosure - Share-Based Compensation - Schedule of Share-Based Compensation Expense (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureSharebasedCompensationScheduleOfSharebasedCompensationExpenseDetails</Role>
      <ShortName>Share-Based Compensation - Schedule of Share-Based Compensation Expense (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>44</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R45.htm</HtmlFileName>
      <LongName>995835 - Disclosure - Income Taxes - Additional Information (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureIncomeTaxesAdditionalInformationDetails</Role>
      <ShortName>Income Taxes - Additional Information (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>45</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R46.htm</HtmlFileName>
      <LongName>995845 - Disclosure - Commitments and Contingencies - Additional Information (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureCommitmentsAndContingenciesAdditionalInformationDetails</Role>
      <ShortName>Commitments and Contingencies - Additional Information (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>46</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R47.htm</HtmlFileName>
      <LongName>995855 - Disclosure - Net Loss Per Share (Additional Information) (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureNetLossPerShareAdditionalInformationDetails</Role>
      <ShortName>Net Loss Per Share (Additional Information) (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>47</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R48.htm</HtmlFileName>
      <LongName>995865 - Disclosure - Net Loss Per Share - Schedule of Number of Ordinary Shares Underlying Potentially Dilutive Securities (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureNetLossPerShareScheduleOfNumberOfOrdinarySharesUnderlyingPotentiallyDilutiveSecuritiesDetails</Role>
      <ShortName>Net Loss Per Share - Schedule of Number of Ordinary Shares Underlying Potentially Dilutive Securities (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>48</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R49.htm</HtmlFileName>
      <LongName>995875 - Disclosure - Related Parties - Additional Information (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureRelatedPartiesAdditionalInformationDetails</Role>
      <ShortName>Related Parties - Additional Information (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>49</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R50.htm</HtmlFileName>
      <LongName>995895 - Disclosure - Earnings Per Share - Additional Information (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureEarningsPerShareAdditionalInformationDetails</Role>
      <ShortName>Earnings Per Share - Additional Information (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>50</Position>
    </Report>
    <Report instance="mura-20240331.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R51.htm</HtmlFileName>
      <LongName>995905 - Disclosure - Subsequent Events - Additional Information (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.muraloncology.com/20240331/taxonomy/role/DisclosureSubsequentEventsAdditionalInformationDetails</Role>
      <ShortName>Subsequent Events - Additional Information (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>51</Position>
    </Report>
    <Report>
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <LongName>All Reports</LongName>
      <ReportType>Book</ReportType>
      <ShortName>All Reports</ShortName>
    </Report>
  </MyReports>
  <InputFiles>
    <File doctype="10-Q" isDefinitelyFs="true" isUsgaap="true" original="mura-20240331.htm">mura-20240331.htm</File>
    <File>mura-20240331.xsd</File>
  </InputFiles>
  <SupplementalFiles/>
  <BaseTaxonomies>
    <BaseTaxonomy items="327">http://fasb.org/us-gaap/2023</BaseTaxonomy>
    <BaseTaxonomy items="30">http://xbrl.sec.gov/dei/2023</BaseTaxonomy>
    <BaseTaxonomy items="12">http://xbrl.sec.gov/ecd/2023</BaseTaxonomy>
  </BaseTaxonomies>
  <HasPresentationLinkbase>false</HasPresentationLinkbase>
  <HasCalculationLinkbase>false</HasCalculationLinkbase>
</FilingSummary>
