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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2015-03-03</periodOfReport>

    <notSubjectToSection16>0</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>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>2015-03-03</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>X</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>2419</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>25007.67</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2419</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Subsidiary</value>
                    <footnoteId id="F1"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Put Option (obligation to buy)</value>
                <footnoteId id="F2"/>
                <footnoteId id="F3"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>25007.67</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2015-03-03</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>X</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>2419</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2015-01-21</value>
            </exerciseDate>
            <expirationDate>
                <value>2015-03-31</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Floating Rate Municipal Term Preferred Shares, Series 2015</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>2419</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Subsidiary</value>
                    <footnoteId id="F1"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Partner Reinsurance Company of the U.S. (&quot;PRC-US&quot;), a wholly owned subsidiary of PartnerRe Ltd., is a direct beneficial owner of the reported securities. PartnerRe Ltd. Is an indirect beneficial owner of the reported securities.. PartnerRe Principal Finance Inc., a wholly owned indirect subsidiary of PartnerRe Ltd., acts as investment adviser for PRC-US and Partner Reinsurance Company Ltd. (&quot;PRC&quot;), a wholly owned direct subsidiary of PartnerRe Ltd.  PartnerRe Principal Finance Inc. and PRC do 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>
        <footnote id="F2">On January 16, 2015, PRC and Citibank N.A. (&quot;Citibank&quot;) entered into a Put/Call Agreement (the &quot;Put/Call Agreement&quot;), by which, among other things, (i) PRC granted Citibank an option (exercisable between January 21, 2015 and March 31, 2015) (the &quot;Put Option&quot;) to cause PRC to purchase the Floating Rate Municipal Term Preferred Shares, Series 2015 (the &quot;MTPS Shares&quot;) from Citibank at the option price of $25,000 per share plus accumulated but unpaid dividends (the &quot;Option Price&quot;); and (ii) Citibank granted PRC an option (exercisable on April 1, 2015) (the &quot;Call Option&quot;) to cause Citibank to sell the MTPS Shares to PRC at the Option Price.  On March 3, 2015, Citibank notified PRC that it was exercising the Put Option.</footnote>
        <footnote id="F3">PRC designated its affiliate, PRC-US, to perform its obligations under the Put/Call Agreement, and accordingly PRC-US purchased the MTPS Shares from Citibank on March 10, 2015 for the Option Price.  The Call Option expired immediately following the exercise of the Put Option, whereupon PRC ceased to be subject to Section 16 of the Exchange Act.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/C. Marc Wetherhill, Chief Legal Counsel</signatureName>
        <signatureDate>2015-05-27</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/C. Marc Wetherhill, General Counsel &amp; Chief Compliance Officer</signatureName>
        <signatureDate>2015-05-27</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/TK Khan, General Counsel</signatureName>
        <signatureDate>2015-05-27</signatureDate>
    </ownerSignature>
</ownershipDocument>
