<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-10-02</periodOfReport>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001471971</rptOwnerCik>
            <rptOwnerName>Cermak Elizabeth</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>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.8074</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2020-10-02</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>40000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <value>2030-10-02</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>40000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>40000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The options set forth in this table vest in three equal annual installments beginning on the first anniversary of the Transaction Date, subject to the grantee's continued service on the Company's Board of Directors on each vesting date.</footnote>
        <footnote id="F2">The options were issued in connection with the reporting person's Board of Director service to the Company.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>/s/ Jonathan Foster by Power of Attorney</signatureName>
        <signatureDate>2020-10-05</signatureDate>
    </ownerSignature>
</ownershipDocument>
