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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

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

    <notSubjectToSection16>1</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001469372</rptOwnerCik>
            <rptOwnerName>MSG NETWORKS INC.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>11 PENNSYLVANIA PLAZA</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10001</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>1</isOther>
            <otherText>See Remarks</otherText>
        </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"/>
                <footnoteId id="F2"/>
                <footnoteId id="F3"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>20397558</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Class B Common Stock, par value $0.01</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.00</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2015-09-30</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
                <footnoteId id="F2"/>
                <footnoteId id="F3"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>4529518.33</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F4"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F4"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock, par value $0.01</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>4529518.33</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">On September 28, 2015, due to an internal distribution of the Common Stock of The Madison Square Garden Company (formerly MSG Spinco, Inc., and referred to herein as &quot;MSG&quot;), a Delaware corporation, to MSG Networks Inc. (formerly The Madison Square Garden Company, and referred to herein as &quot;MSG Networks&quot;), a Delaware corporation, by certain wholly owned subsidiaries of MSG Networks, MSG Networks became the direct owner of the 1,000 shares of Common Stock of MSG.  This internal distribution was exempt from Section 16 of the Securities Exchange Act of 1934, as amended (the &quot;Exchange Act&quot;) pursuant to Rule 16a-13 under the Exchange Act.</footnote>
        <footnote id="F2">Pursuant to the Amended and Restated Certificate of Incorporation of MSG filed by MSG with the Secretary of the State of Delaware on September 30, 2015, at 11:59 p.m. on September 30, 2015, the 1,000 outstanding shares of common stock of MSG were automatically converted into an aggregate of 20,397,558 fully-paid and nonassessable shares of Class A Common Stock of MSG and 4,529,518.33 fully-paid and nonassessable shares of Class B Common Stock of MSG (the &quot;Recapitalization&quot;). The Recapitalization was exempt pursuant to Rules 16a-9 and 16b-7 under the Exchange Act and did not result in a change in the pecuniary interest of MSG Networks in MSG.</footnote>
        <footnote id="F3">On September 30, 2015, 20,397,558 shares of Class A Common Stock of MSG and 4,529,518.33 shares of Class B Common Stock of MSG were distributed by MSG Networks by way of a pro rata dividend to its stockholders (the &quot;Distribution&quot;), which was exempt from Section 16 pursuant to Rule 16a-9 under the Exchange Act. As a result of the Distribution, MSG Networks no longer beneficially owns any shares of MSG and consequently is no longer subject to the requirements of Section 16 of the Exchange Act with respect to MSG.</footnote>
        <footnote id="F4">Class B Common Stock is convertible at the option of the holder on a one-for-one basis into Class A Common Stock of MSG.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Lawrence J. Burian, Executive Vice President, General Counsel and Secretary of MSG Networks Inc.</signatureName>
        <signatureDate>2015-10-01</signatureDate>
    </ownerSignature>
</ownershipDocument>
