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Note 7 - Income Taxes - Summary of Valuation Allowance (Details) - USD ($) $ in Thousands | 12 Months Ended
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Dec. 31, 2022 | Dec. 31, 2021
Valuation allowance at beginning of period | $ 18,823 | $ 13,867
Income tax benefit | 6,873 | 4,956
Release of valuation allowance | 0 | 0
Valuation allowance at end of period | $ 25,696 | $ 18,823

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- Definition Represents valuation allowance releases for deferred tax assets. + References No definition available. + Details
Name: | mbrx_DeferredTaxAssetsValuationAllowanceReleases
Namespace Prefix: | mbrx_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | duration

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- Definition Amount of deferred tax assets for which it is more likely than not that a tax benefit will not be realized. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 740 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (c) -URI https://asc.fasb.org/extlink&oid=121826272&loc=d3e32537-109319 + Details
Name: | us-gaap_DeferredTaxAssetsValuationAllowance
Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | instant

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- Definition Amount of increase (decrease) in the valuation allowance for a specified deferred tax asset. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 740 -SubTopic 10 -Section 50 -Paragraph 2 -URI https://asc.fasb.org/extlink&oid=121826272&loc=d3e32537-109319 + Details
Name: | us-gaap_ValuationAllowanceDeferredTaxAssetChangeInAmount
Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | duration