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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2015-09-30</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001636519</issuerCik>
        <issuerName>Madison Square Garden Co</issuerName>
        <issuerTradingSymbol>MSG</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001042445</rptOwnerCik>
            <rptOwnerName>TESE VINCENT</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>TWO PENNSYLVANIA PLAZA</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10121</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock, par value $0.01</value>
            </securityTitle>
            <transactionDate>
                <value>2015-09-30</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>6163</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>6411</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Includes 6,163 shares of Class A Common Stock received by the Reporting Person in connection with the distribution by MSG Networks Inc. (formerly, The Madison Square Garden Company, and referred to herein as &quot;MSG Networks&quot;) of all of the outstanding common stock of The Madison Square Garden Company (formerly, MSG Spinco, Inc. and referred to herein as &quot;MSG&quot;) to its stockholders (the &quot;Distribution&quot;)  pursuant to vested MSG Networks restricted stock units.  The shares of Class A Common Stock were granted pursuant to the 2015 Stock Plan for Non-Employee Directors.</footnote>
        <footnote id="F2">Includes shares of MSG Class A Common Stock received in connection with the Distribution in an exempt transaction under Rule 16b-3 and 16a-9.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Mark C. Cresitello, Attorney-in-Fact for Vincent Tese</signatureName>
        <signatureDate>2015-10-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
