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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2012-12-17</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0001093082</issuerCik>
        <issuerName>HUTTIG BUILDING PRODUCTS INC</issuerName>
        <issuerTradingSymbol>HBPLPK</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001076378</rptOwnerCik>
            <rptOwnerName>CEMEX SAB DE CV</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>AVENIDA RICARDO MARGAIN ZOZAYA 325,</rptOwnerStreet1>
            <rptOwnerStreet2>COLONIA VALLE DEL CAMPESTRE</rptOwnerStreet2>
            <rptOwnerCity>SAN PEDRO GARZA GARCIA N. LEON</rptOwnerCity>
            <rptOwnerState>O5</rptOwnerState>
            <rptOwnerZipCode>66265</rptOwnerZipCode>
            <rptOwnerStateDescription>MEXICO</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001100921</rptOwnerCik>
            <rptOwnerName>RUGBY GROUP LTD</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>CEMEX HOUSE, COLDHARBOUR LANE</rptOwnerStreet1>
            <rptOwnerStreet2>THORPE, EGHAM</rptOwnerStreet2>
            <rptOwnerCity>SURREY</rptOwnerCity>
            <rptOwnerState>X0</rptOwnerState>
            <rptOwnerZipCode>TW20 8TD</rptOwnerZipCode>
            <rptOwnerStateDescription>UNITED KINGDOM</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 $0.01 per share</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <transactionDate>
                <value>2012-12-17</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>5755940</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>1.10</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">This form is a joint filing by CEMEX S.A.B. de C.V. (&quot;CEMEX&quot;) and The Rugby Group Limited (&quot;Rugby&quot;), each of whom is filing in its capacity as a 10% owner.</footnote>
        <footnote id="F2">The Shares were held by Rugby. As Rugby is an indirect wholly-owned subsidiary of CEMEX, CEMEX may be deemed to beneficially own the Shares.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Guillermo F. Hernandez Morales, Attorney, CEMEX S.A.B. de C.V.</signatureName>
        <signatureDate>2012-12-18</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Michael F. Egan, Vice President, The Rugby Group Limited</signatureName>
        <signatureDate>2012-12-18</signatureDate>
    </ownerSignature>
</ownershipDocument>
