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

    <schemaVersion>X0306</schemaVersion>

    <documentType>5</documentType>

    <periodOfReport>2019-12-31</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <form3HoldingsReported>0</form3HoldingsReported>

    <form4TransactionsReported>0</form4TransactionsReported>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000935761</rptOwnerCik>
            <rptOwnerName>DOLAN CHARLES F</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O DOLAN FAMILY OFFICE</rptOwnerStreet1>
            <rptOwnerStreet2>340 CROSSWAYS PARK DRIVE</rptOwnerStreet2>
            <rptOwnerCity>WOODBURY</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>11797</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>1</isOther>
            <otherText>Member of 13D Group</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000902298</rptOwnerCik>
            <rptOwnerName>DOLAN HELEN A</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O DOLAN FAMILY OFFICE</rptOwnerStreet1>
            <rptOwnerStreet2>340 CROSSWAYS PARK DRIVE</rptOwnerStreet2>
            <rptOwnerCity>WOODBURY</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>11797</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>1</isOther>
            <otherText>Member of 13D Group</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001723920</rptOwnerCik>
            <rptOwnerName>Charles F. Dolan 2009 Revocable Trust</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O DOLAN FAMILY OFFICE</rptOwnerStreet1>
            <rptOwnerStreet2>340 CROSSWAYS PARK DRIVE</rptOwnerStreet2>
            <rptOwnerCity>WOODBURY</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>11797</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <otherText>Member of 13D Group</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
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            <transactionDate>
                <value>2019-12-17</value>
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                <natureOfOwnership>
                    <value>By CFD 2018 GRAT #1M</value>
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                    <value>By CFD 2009 Revocable Trust</value>
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                </underlyingSecurityTitle>
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                </underlyingSecurityShares>
            </underlyingSecurity>
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                <sharesOwnedFollowingTransaction>
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                    <footnoteId id="F6"/>
                    <footnoteId id="F7"/>
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                <natureOfOwnership>
                    <value>By HAD 2018 GRAT #1M</value>
                </natureOfOwnership>
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        </derivativeTransaction>
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            <securityTitle>
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                    <value>By HAD 2009 Revocable Trust</value>
                </natureOfOwnership>
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                <footnoteId id="F1"/>
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                    <footnoteId id="F9"/>
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                    <value>By CFD 2019 GRAT #1M</value>
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                <footnoteId id="F1"/>
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                    <value>I</value>
                    <footnoteId id="F6"/>
                    <footnoteId id="F8"/>
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                <natureOfOwnership>
                    <value>By HAD 2009 Revocable Trust</value>
                </natureOfOwnership>
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        <derivativeTransaction>
            <securityTitle>
                <value>Class B Common Stock</value>
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                <footnoteId id="F1"/>
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            <transactionDate>
                <value>2019-12-23</value>
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                <transactionFormType>5</transactionFormType>
                <transactionCode>G</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
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                <value></value>
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                    <value>56056</value>
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                <transactionPricePerShare>
                    <value>0.00</value>
                    <footnoteId id="F2"/>
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                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
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            <exerciseDate>
                <footnoteId id="F1"/>
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            <expirationDate>
                <footnoteId id="F1"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>56056</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
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                <sharesOwnedFollowingTransaction>
                    <value>56056</value>
                </sharesOwnedFollowingTransaction>
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                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F6"/>
                    <footnoteId id="F10"/>
                </directOrIndirectOwnership>
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                    <value>By HAD 2019 GRAT #1M</value>
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    <footnotes>
        <footnote id="F1">The Madison Square Garden Company Class B Common Stock (the &quot;Class B Common Stock&quot;) of the Issuer is convertible at the option of the holder on a share for share basis into The Madison Square Garden Company Class A Common Stock (the &quot;Class A Common Stock&quot;) of the Issuer.</footnote>
        <footnote id="F2">Gift.</footnote>
        <footnote id="F3">Helen A. Dolan disclaims beneficial ownership of these securities and this report shall not be deemed to be an admission that she is, for purposes of Section 16 or for any other purpose, the beneficial owner of such securities.</footnote>
        <footnote id="F4">These securities are owned solely by the Charles F. Dolan 2018 Grantor Retained Annuity Trust #1M. Charles F. Dolan is the sole trustee and beneficiary of the trust.</footnote>
        <footnote id="F5">Charles F. Dolan is a co-trustee and beneficiary of the Charles F. Dolan 2009 Revocable Trust.</footnote>
        <footnote id="F6">Charles F. Dolan disclaims beneficial ownership of these securities and this report shall not be deemed to be an admission that he is, for purposes of Section 16 or for any other purpose, the beneficial owner of such securities.</footnote>
        <footnote id="F7">These securities are owned solely by the Helen A. Dolan 2018 Grantor Retained Annuity Trust #1M. Helen A. Dolan is the sole trustee and beneficiary of the trust.</footnote>
        <footnote id="F8">Helen A. Dolan is a co-trustee and beneficiary of the Helen A. Dolan 2009 Revocable Trust.</footnote>
        <footnote id="F9">These securities are owned solely by the Charles F. Dolan 2019 Grantor Retained Annuity Trust #1M. Charles F. Dolan is the sole trustee and beneficiary of the trust.</footnote>
        <footnote id="F10">These securities are owned solely by the Helen A. Dolan 2019 Grantor Retained Annuity Trust #1M. Helen A. Dolan is the sole trustee and beneficiary of the trust.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Dennis H. Javer, as Attorney-in-Fact for Charles F. Dolan</signatureName>
        <signatureDate>2020-02-14</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Dennis H. Javer, as Attorney-in-Fact for Helen A. Dolan</signatureName>
        <signatureDate>2020-02-14</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>CHARLES F. DOLAN 2009 REVOCABLE TRUST By: /s/ Dennis H. Javer, as Attorney-in-Fact</signatureName>
        <signatureDate>2020-02-14</signatureDate>
    </ownerSignature>
</ownershipDocument>
