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

    <schemaVersion>X0303</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2009-03-03</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000944765</issuerCik>
        <issuerName>MERGE HEALTHCARE Inc</issuerName>
        <issuerTradingSymbol>MRGE</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001437683</rptOwnerCik>
            <rptOwnerName>Merrick RIS, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>233 NORTH MICHIGAN AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 2330</rptOwnerStreet2>
            <rptOwnerCity>CHICAGO</rptOwnerCity>
            <rptOwnerState>IL</rptOwnerState>
            <rptOwnerZipCode>60601</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001163431</rptOwnerCik>
            <rptOwnerName>FERRO MICHAEL W JR</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>233 NORTH MICHIGAN AVENUE,</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 2330</rptOwnerStreet2>
            <rptOwnerCity>CHICAGO</rptOwnerCity>
            <rptOwnerState>IL</rptOwnerState>
            <rptOwnerZipCode>60601</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2009-03-03</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>5600</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>1.25</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>28089137</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes></footnotes>

    <remarks>The reporting persons are Merrick RIS, LLC (&quot;Merrick&quot;), a Delaware limited liability company, and Michael W. Ferro, Jr. (&quot;Mr. Ferro&quot;), the Chairman of the Board of Directors of Merge Healthcare Incorporated (&quot;Merge&quot;).  Mr. Ferro has sole voting and investment power with respect to the Merge Common Stock held by Merrick and, accordingly, may be deemed for purposes of Rule 13d-3 of the Securities and Exchange Act of 1934, as amended, the beneficial owner of securities held by Merrick.  The address of the reporting persons is 233 North Michigan Avenue, Suite 2330, Chicago, Illinois 60601.</remarks>

    <ownerSignature>
        <signatureName>Julie Ann B. Schumitsch, by Power of Attorney for Merrick RIS, LLC</signatureName>
        <signatureDate>2009-03-05</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Julie Ann B. Schumitsch, by Power of Attorney for Michael W. Ferro, Jr.</signatureName>
        <signatureDate>2009-03-05</signatureDate>
    </ownerSignature>
</ownershipDocument>
