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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

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

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0000846596</issuerCik>
        <issuerName>DEUTSCHE STRATEGIC MUNICIPAL INCOME TRUST</issuerName>
        <issuerTradingSymbol>KSM</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>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>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001643277</rptOwnerCik>
            <rptOwnerName>Partner Reinsurance Co of the U.S.</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>2419</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>25025.62</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 $25,000 per share plus accumulated but unpaid dividends.</footnote>
        <footnote id="F2">Partner Reinsurance Company of the U.S. (&quot;PRC-US&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-US. 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 (the &quot;Exchange Act&quot;).</footnote>
    </footnotes>

    <remarks></remarks>

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

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

    <ownerSignature>
        <signatureName>/s/Thomas L. Forsyth, EVP, General Counsel &amp; Corporate Secretary</signatureName>
        <signatureDate>2015-06-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
