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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2015-06-01</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0000839533</issuerCik>
        <issuerName>DEUTSCHE MUNICIPAL INCOME TRUST</issuerName>
        <issuerTradingSymbol>KTF</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000911421</rptOwnerCik>
            <rptOwnerName>PARTNERRE LTD</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>90 PITTS BAY RD.</rptOwnerStreet1>
            <rptOwnerStreet2>WELLESLEY HOUSE</rptOwnerStreet2>
            <rptOwnerCity>PEMBROKE</rptOwnerCity>
            <rptOwnerState>D0</rptOwnerState>
            <rptOwnerZipCode>HM08</rptOwnerZipCode>
            <rptOwnerStateDescription>BERMUDA</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001643270</rptOwnerCik>
            <rptOwnerName>Partner Reinsurance Co Ltd.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>90 PITTS BAY RD.</rptOwnerStreet1>
            <rptOwnerStreet2>WELLESLEY HOUSE</rptOwnerStreet2>
            <rptOwnerCity>PEMBROKE</rptOwnerCity>
            <rptOwnerState>D0</rptOwnerState>
            <rptOwnerZipCode>HM08</rptOwnerZipCode>
            <rptOwnerStateDescription>BERMUDA</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001599479</rptOwnerCik>
            <rptOwnerName>PartnerRe Principal Finance Inc.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>ONE GREENWICH PLAZA</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>GREENWICH</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06830</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Floating Rate Municipal Term Preferred Shares, Series 2015</value>
            </securityTitle>
            <transactionDate>
                <value>2015-06-01</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>37773</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>5005.16</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Subsidiary</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The reported securities were called for redemption by the issuer at $5,000 per share plus accumulated but unpaid dividends.</footnote>
        <footnote id="F2">Partner Reinsurance Company Ltd. (&quot;PRC&quot;), a wholly owned subsidiary of PartnerRe Ltd., was a direct beneficial owner of the reported securities. PartnerRe Ltd. was an indirect beneficial owner of the reported securities. PartnerRe Principal Finance Inc., a wholly owned indirect subsidiary of PartnerRe Ltd., acted as investment adviser for PRC.  PartnerRe Principal Finance Inc. did not beneficially own any of the reported securities within the meaning of Rule 16a-1(a)(2) under the Securities Exchange Act of 1934.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/C. Marc Wetherhill, Chief Legal Counsel</signatureName>
        <signatureDate>2015-06-02</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/C. Marc Wetherhill, General Counsel &amp; Chief Compliance Officer</signatureName>
        <signatureDate>2015-06-02</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/TK Khan, General Counsel</signatureName>
        <signatureDate>2015-06-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
