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

    <schemaVersion>X0303</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2009-09-09</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000056047</issuerCik>
        <issuerName>KIRBY CORP</issuerName>
        <issuerTradingSymbol>KEX</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001203119</rptOwnerCik>
            <rptOwnerName>DAY C SEAN</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>26 DEER PARK DRIVE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>GREENWICH</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06830</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, par value $.10 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2009-09-09</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>19500</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>38.5658</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>29382</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">The reported price is the weighted average purchase price.  The purchases were made at prices ranging from $38.3912 to $38.7014 per share.  The reporting person will provide, upon request by the Commission staff, the issuer or a stockholder of the issuer, full information regarding the number of shares purchased at each separate price.</footnote>
        <footnote id="F2">On September 8, 2009, a grantor retained annuity trust for the benefit of the reporting person and another family trust transferred 14,883 shares of Kirby Corporation common stock to the reporting person.  Those shares are now reported as directly owned instead of indirectly owned.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>G. Stephen Holcomb, Agent and Attorney-in-Fact</signatureName>
        <signatureDate>2009-09-11</signatureDate>
    </ownerSignature>
</ownershipDocument>
