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

    <schemaVersion>X0304</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2012-01-11</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000877463</issuerCik>
        <issuerName>Invesco Van Kampen Municipal Trust</issuerName>
        <issuerTradingSymbol>VKQ</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000070858</rptOwnerCik>
            <rptOwnerName>BANK OF AMERICA CORP /DE/</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>BANK OF AMERICA CORPORATE CENTER</rptOwnerStreet1>
            <rptOwnerStreet2>100 N TRYON ST</rptOwnerStreet2>
            <rptOwnerCity>CHARLOTTE</rptOwnerCity>
            <rptOwnerState>NC</rptOwnerState>
            <rptOwnerZipCode>28255</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001102113</rptOwnerCik>
            <rptOwnerName>BANK OF AMERICA NA</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>101 S TRYON STREET</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>CHARLOTTE</rptOwnerCity>
            <rptOwnerState>NC</rptOwnerState>
            <rptOwnerZipCode>28255</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001453700</rptOwnerCik>
            <rptOwnerName>Blue Ridge Investments, L.L.C.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>214 NORTH TRYON STREET</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>CHARLOTTE</rptOwnerCity>
            <rptOwnerState>NC</rptOwnerState>
            <rptOwnerZipCode>28255</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Auction Rate Preferred</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <transactionDate>
                <value>2012-01-11</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F2"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>80</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1635</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F1"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Auction Rate Preferred</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <transactionDate>
                <value>2012-01-12</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F2"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>23</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1612</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F1"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">The Auction Rate Preferred Shares (&quot;Shares&quot;) reported in Table I represent shares beneficially owned by Bank of America N.A. (&quot;BANA&quot;) and Blue Ridge Investors, L.L.C. (&quot;Blue Ridge&quot;). BANA and Blue Ridge are wholly owned subsidiaries of Bank of America Corporation (&quot;Bank of America&quot;).</footnote>
        <footnote id="F2">The Shares were called for redemption by the issuer at par value.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ John Hiebendahl</signatureName>
        <signatureDate>2012-01-13</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Michael Didovic</signatureName>
        <signatureDate>2012-01-13</signatureDate>
    </ownerSignature>
</ownershipDocument>
