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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-07-22</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001058090</issuerCik>
        <issuerName>CHIPOTLE MEXICAN GRILL INC</issuerName>
        <issuerTradingSymbol>CMG</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001282797</rptOwnerCik>
            <rptOwnerName>WINSTON MARY A</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CHIPOTLE MEXICAN GRILL</rptOwnerStreet1>
            <rptOwnerStreet2>610 NEWPORT CENTER DR</rptOwnerStreet2>
            <rptOwnerCity>NEWPORT BEACH</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>92660</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common  stock</value>
            </securityTitle>
            <transactionDate>
                <value>2020-07-22</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>107</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>107</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The reporting person received a prorated grant of restricted stock units (&quot;RSUs&quot;) under the Amended and Restated Chipotle Mexican Grill, Inc. 2011 Stock Incentive Plan and Chipotle's Director Compensation Program in connection with her election to the Board on July 17, 2020.  The RSUs cover her term of service from July 17, 2020 to Chipotle's 2021 annual meeting of shareholders. The RSUs will settle in shares of Chipotle common stock on a one-for-one basis and will vest in full on May 21, 2021, subject to the reporting person's continued service on the Chipotle Board of Directors.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Helen Kaminski, pursuant to the power of attorney previously filed</signatureName>
        <signatureDate>2020-07-24</signatureDate>
    </ownerSignature>
</ownershipDocument>
