<SEC-DOCUMENT>0001659617-20-000173.txt : 20200707
<SEC-HEADER>0001659617-20-000173.hdr.sgml : 20200707
<ACCEPTANCE-DATETIME>20200707172447
ACCESSION NUMBER:		0001659617-20-000173
CONFORMED SUBMISSION TYPE:	4
PUBLIC DOCUMENT COUNT:		1
CONFORMED PERIOD OF REPORT:	20200702
FILED AS OF DATE:		20200707
DATE AS OF CHANGE:		20200707

REPORTING-OWNER:	

	OWNER DATA:	
		COMPANY CONFORMED NAME:			KLEMP WALTER V
		CENTRAL INDEX KEY:			0000938419

	FILING VALUES:
		FORM TYPE:		4
		SEC ACT:		1934 Act
		SEC FILE NUMBER:	001-37758
		FILM NUMBER:		201016682

	MAIL ADDRESS:	
		STREET 1:		1415 WEST LOOP NORTH
		CITY:			HOUSTON
		STATE:			TX
		ZIP:			77055

ISSUER:		

	COMPANY DATA:	
		COMPANY CONFORMED NAME:			Moleculin Biotech, Inc.
		CENTRAL INDEX KEY:			0001659617
		STANDARD INDUSTRIAL CLASSIFICATION:	PHARMACEUTICAL PREPARATIONS [2834]
		IRS NUMBER:				474671999
		STATE OF INCORPORATION:			DE
		FISCAL YEAR END:			1231

	BUSINESS ADDRESS:	
		STREET 1:		5300 MEMORIAL DRIVE
		STREET 2:		SUITE 950
		CITY:			HOUSTON
		STATE:			TX
		ZIP:			77007
		BUSINESS PHONE:		713-300-5160

	MAIL ADDRESS:	
		STREET 1:		5300 MEMORIAL DRIVE
		STREET 2:		SUITE 950
		CITY:			HOUSTON
		STATE:			TX
		ZIP:			77007
</SEC-HEADER>
<DOCUMENT>
<TYPE>4
<SEQUENCE>1
<FILENAME>wf-form4_159415661342622.xml
<DESCRIPTION>FORM 4
<TEXT>
<XML>
<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-07-02</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001659617</issuerCik>
        <issuerName>Moleculin Biotech, Inc.</issuerName>
        <issuerTradingSymbol>MBRX</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000938419</rptOwnerCik>
            <rptOwnerName>KLEMP WALTER V</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O MOLECULIN BIOTECH, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>5300 MEMORIAL DR., SUITE 950</rptOwnerStreet2>
            <rptOwnerCity>HOUSTON</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>77007</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>CEO and President</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable></nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.928</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2020-07-02</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>500000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <value>2030-07-02</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>500000.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2156907</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Restricted Stock Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F3"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2020-07-02</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>353211</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F4"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F4"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>353211.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2510118</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">(1) The stock option set forth in this table vests in four equal annual installments beginning on the first anniversary of the Transaction Date, subject to the grantee's continued service to the Company on each vesting date.</footnote>
        <footnote id="F2">(2) Issued in connection with the reporting person's employment with the Company.</footnote>
        <footnote id="F3">(3) Each restricted stock unit represents a contingent right to receive one share of Company common stock.</footnote>
        <footnote id="F4">(4) The restricted stock units set forth in this table vests in four equal annual installments beginning on the first anniversary of the Transaction Date, subject to the grantee's continued service to the Company on each vesting date.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Walter Klemp</signatureName>
        <signatureDate>2020-07-07</signatureDate>
    </ownerSignature>
</ownershipDocument>
</XML>
</TEXT>
</DOCUMENT>
</SEC-DOCUMENT>
