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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-02-22</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001692718</rptOwnerCik>
            <rptOwnerName>Namvar Ali</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CHIPOTLE MEXICAN GRILL, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>1401 WYNKOOP STREET, SUITE 500</rptOwnerStreet2>
            <rptOwnerCity>DENVER</rptOwnerCity>
            <rptOwnerState>CO</rptOwnerState>
            <rptOwnerZipCode>80202</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>2018-02-22</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>3000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>317.70</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3000</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The reporting person disclaims beneficial ownership of the securities of the Issuer reported as beneficially owned by Pershing Square Capital Management L.P., PS Management GP, LLC and William A. Ackman, and accordingly this report does not include such securities.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Michael McGawn, as attorney-in-fact</signatureName>
        <signatureDate>2018-02-23</signatureDate>
    </ownerSignature>
</ownershipDocument>
