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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2014-07-08</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001071993</issuerCik>
        <issuerName>CONTANGO OIL &amp; GAS CO</issuerName>
        <issuerTradingSymbol>MCF</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001060479</rptOwnerCik>
            <rptOwnerName>SCHOONOVER STEVEN L</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CONTANGO OIL &amp; GAS COMPANY</rptOwnerStreet1>
            <rptOwnerStreet2>717 TEXAS AVENUE, SUITE 2900</rptOwnerStreet2>
            <rptOwnerCity>HOUSTON</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>77002</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</value>
            </securityTitle>
            <transactionDate>
                <value>2014-07-08</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>2612</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>67582</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Represents a grant of restricted stock pursuant to the Issuer's 2009 Equity Compensation Plan.  Subject to the terms of the restricted stock award agreement, the stock grant vests 100% on July 8, 2015, the one-year anniversary of the date of grant.</footnote>
    </footnotes>

    <remarks>This Form 4 has been signed by John A. Thomas, Secretary of Contango Oil &amp; Gas Company, on behalf of Mr. Schoonover, pursuant to an instrument of power of attorney, dated October 1, 2013.  The authority granted pursuant to such instrument is to remain in full force and effect until rescinded in writing by Mr. Schoonover.</remarks>

    <ownerSignature>
        <signatureName>/s/ John A. Thomas</signatureName>
        <signatureDate>2014-07-10</signatureDate>
    </ownerSignature>
</ownershipDocument>
