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

    <schemaVersion>X0304</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2012-02-28</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001089907</issuerCik>
        <issuerName>SWK Holdings Corp</issuerName>
        <issuerTradingSymbol>NONE</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001056973</rptOwnerCik>
            <rptOwnerName>CARLSON CAPITAL L P</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2100 MCKINNEY AVE</rptOwnerStreet1>
            <rptOwnerStreet2>STE 1800</rptOwnerStreet2>
            <rptOwnerCity>DALLAS</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>75201</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001452364</rptOwnerCik>
            <rptOwnerName>Black Diamond Offshore Ltd.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2100 MCKINNEY AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 1800</rptOwnerStreet2>
            <rptOwnerCity>DALLAS</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>75201</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001404976</rptOwnerCik>
            <rptOwnerName>Double Black Diamond Offshore Ltd</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2100 MCKINNEY AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 1800</rptOwnerStreet2>
            <rptOwnerCity>DALLAS</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>75201</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001404557</rptOwnerCik>
            <rptOwnerName>Asgard Investment Corp.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2100 MCKINNEY AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 1800</rptOwnerStreet2>
            <rptOwnerCity>DALLAS</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>75201</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001404625</rptOwnerCik>
            <rptOwnerName>Carlson Clint Duane</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2100 MCKINNEY AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 1800</rptOwnerStreet2>
            <rptOwnerCity>DALLAS</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>75201</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001449554</rptOwnerCik>
            <rptOwnerName>Black Diamond Relative Value Offshore Ltd.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2100 MCKINNEY AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 1800</rptOwnerStreet2>
            <rptOwnerCity>DALLAS</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>75201</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, par value $0.001 per share (the &quot;Common Stock&quot;</value>
            </securityTitle>
            <transactionDate>
                <value>2012-02-28</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>500000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.82</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>12149100</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">The shares of Common Stock to which this relates are held directly by Black Diamond Offshore Ltd., a Cayman Islands exempted company (&quot;Offshore&quot;) and Double Black Diamond Offshore Ltd., a Cayman Islands exempted company (&quot;Double Offshore&quot; and together with Offshore, the &quot;Funds&quot;).</footnote>
        <footnote id="F2">Carlson Capital, L.P., a Delaware limited partnership (&quot;Carlson Capital&quot;) serves as the investment manager to, and has the power to direct the affairs of, the Funds. Asgard Investment Corp., a Delaware corporation (&quot;Asgard&quot;) serves as the indirect general partner of, and has the power to direct the affairs of, Carlson Capital. Mr. Clint D. Carlson, a U.S. citizen, serves as the president of, and has the power to direct the affairs of, Asgard and Carlson Capital.  Each of the reporting persons disclaims beneficial ownership of the securities to which this Form 4 relates for the purposes of Section 16 of the Securities and Exchange Act of 1934, as amended, except as to such extent of the reporting person's pecuniary interest in the securities.</footnote>
        <footnote id="F3">Excludes 235,000 shares of restricted stock beneficially owned by Michael D. Weinberg, an employee of Carlson Capital, in his capacity as a director of SWK Holdings Corporation.  Each of the Funds, Carlson Capital, Asgard and Mr. Carlson expressly disclaims beneficial ownership of the 235,000 shares of restricted stock beneficially owned by Michael D. Weinberg.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Carlson Capital, L.P., By: /s/ Clint D. Carlson, President</signatureName>
        <signatureDate>2012-03-01</signatureDate>
    </ownerSignature>
</ownershipDocument>
