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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2013-06-14</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001362925</issuerCik>
        <issuerName>Planet Payment Inc</issuerName>
        <issuerTradingSymbol>PLPM</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001565230</rptOwnerCik>
            <rptOwnerName>Kim Shane H.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CAMDEN PARTNERS HOLDINGS, LLC</rptOwnerStreet1>
            <rptOwnerStreet2>500 EAST PRATT STREET SUITE 1200</rptOwnerStreet2>
            <rptOwnerCity>BALTIMORE</rptOwnerCity>
            <rptOwnerState>MD</rptOwnerState>
            <rptOwnerZipCode>21202</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>See Remarks</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001365552</rptOwnerCik>
            <rptOwnerName>Camden Partners Strategic Manager, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CAMDEN PARTNERS HOLDINGS, LLC</rptOwnerStreet1>
            <rptOwnerStreet2>500 EAST PRATT STREET SUITE 1200</rptOwnerStreet2>
            <rptOwnerCity>BALTIMORE</rptOwnerCity>
            <rptOwnerState>MD</rptOwnerState>
            <rptOwnerZipCode>21202</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>Affiliated with Shane H. Kim</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001317017</rptOwnerCik>
            <rptOwnerName>Camden Partners Strategic III, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CAMDEN PARTNERS HOLDINGS, LLC</rptOwnerStreet1>
            <rptOwnerStreet2>500 EAST PRATT STREET SUITE 1200</rptOwnerStreet2>
            <rptOwnerCity>BALTIMORE</rptOwnerCity>
            <rptOwnerState>MD</rptOwnerState>
            <rptOwnerZipCode>21202</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>Affiliated with Shane H. Kim</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001160267</rptOwnerCik>
            <rptOwnerName>CAMDEN PARTNERS STRATEGIC II LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CAMDEN PARTNERS HOLDINGS, LLC</rptOwnerStreet1>
            <rptOwnerStreet2>500 EAST PRATT STREET SUITE 1200</rptOwnerStreet2>
            <rptOwnerCity>BALTIMORE</rptOwnerCity>
            <rptOwnerState>MD</rptOwnerState>
            <rptOwnerZipCode>21202</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>Affiliated with Shane H. Kim</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001283497</rptOwnerCik>
            <rptOwnerName>CAMDEN PARTNERS STRATEGIC FUND III LP</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CAMDEN PARTNERS HOLDINGS, LLC</rptOwnerStreet1>
            <rptOwnerStreet2>500 EAST PRATT STREET SUITE 1200</rptOwnerStreet2>
            <rptOwnerCity>BALTIMORE</rptOwnerCity>
            <rptOwnerState>MD</rptOwnerState>
            <rptOwnerZipCode>21202</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>Affiliated with Shane H. Kim</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001283498</rptOwnerCik>
            <rptOwnerName>CAMDEN PARTNERS STRATEGIC FUND III-A LP</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CAMDEN PARTNERS HOLDINGS, LLC</rptOwnerStreet1>
            <rptOwnerStreet2>500 EAST PRATT STREET SUITE 1200</rptOwnerStreet2>
            <rptOwnerCity>BALTIMORE</rptOwnerCity>
            <rptOwnerState>MD</rptOwnerState>
            <rptOwnerZipCode>21202</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>Affiliated with Shane H. Kim</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001157600</rptOwnerCik>
            <rptOwnerName>CAMDEN PARTNERS STRATEGIC FUND II A LP</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CAMDEN PARTNERS HOLDINGS, LLC</rptOwnerStreet1>
            <rptOwnerStreet2>500 EAST PRATT STREET SUITE 1200</rptOwnerStreet2>
            <rptOwnerCity>BALTIMORE</rptOwnerCity>
            <rptOwnerState>MD</rptOwnerState>
            <rptOwnerZipCode>21202</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>Affiliated with Shane H. Kim</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001211897</rptOwnerCik>
            <rptOwnerName>CAMDEN PARTNERS STRATEGIC FUND II B LP</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CAMDEN PARTNERS HOLDINGS, LLC</rptOwnerStreet1>
            <rptOwnerStreet2>500 EAST PRATT STREET SUITE 1200</rptOwnerStreet2>
            <rptOwnerCity>BALTIMORE</rptOwnerCity>
            <rptOwnerState>MD</rptOwnerState>
            <rptOwnerZipCode>21202</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>Affiliated with Shane H. Kim</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001025664</rptOwnerCik>
            <rptOwnerName>WARNOCK DAVID L</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CAMDEN PARTNERS HOLDINGS, LLC</rptOwnerStreet1>
            <rptOwnerStreet2>500 EAST PRATT STREET SUITE 1200</rptOwnerStreet2>
            <rptOwnerCity>BALTIMORE</rptOwnerCity>
            <rptOwnerState>MD</rptOwnerState>
            <rptOwnerZipCode>21202</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>Affiliated with Shane H. Kim</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001211899</rptOwnerCik>
            <rptOwnerName>HUGHES DONALD W</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CAMDEN PARTNERS HOLDINGS, LLC</rptOwnerStreet1>
            <rptOwnerStreet2>500 EAST PRATT STREET SUITE 1200</rptOwnerStreet2>
            <rptOwnerCity>BALTIMORE</rptOwnerCity>
            <rptOwnerState>MD</rptOwnerState>
            <rptOwnerZipCode>21202</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>Affiliated with Shane H. Kim</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2013-06-14</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>21818</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>21818</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2013-06-14</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>0</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1997513</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2013-06-14</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>0</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>118496</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2013-06-14</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>0</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4446267</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2013-06-14</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>0</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>184780</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F5"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">This is a restricted stock grant under the Issuer's 2012 Equity Incentive Plan.  The shares will be fully vested on June 14, 2014, and will be subject to forfeiture if Mr. Kim resigns or is removed as director before such date.</footnote>
        <footnote id="F2">These securities are owned directly by Fund II-A.  The Reporting Person, CPSM, CPS III, CPS II, Fund III, Fund III-A, Fund II-B and the Managing Members may be deemed indirect beneficial owners of the securities held directly by Fund II-A as a result of their relationships described in the Remarks (below).  The Reporting Person, CPSM, CPS III, CPS II, Fund III, Fund III-A, and Fund II-B and each of the Managing Members disclaim beneficial ownership of the securities held directly by Fund II-A, except to the extent of their respective pecuniary interests therein.</footnote>
        <footnote id="F3">These securities are owned directly by Fund II-B.  The Reporting Person, CPSM, CPS III, CPS II, Fund III, Fund III-A, Fund II-A and the Managing Members may be deemed indirect beneficial owners of the securities held directly by Fund II-B as a result of their relationships described in the Remarks (below).  The Reporting Person, CPSM, CPS III, CPS II, Fund III, Fund III-A, and Fund II-A and each of the Managing Members disclaim beneficial ownership of the securities held directly by Fund II-B, except to the extent of their respective pecuniary interests therein.</footnote>
        <footnote id="F4">These securities are owned directly by Fund III.  The Reporting Person, CPSM, CPS III, CPS II, Fund III-A, Fund II-A, Fund II-B and the Managing Members may be deemed indirect beneficial owners of the securities held directly by Fund III as a result of their relationships described in the Remarks (below).  The Reporting Person, CPSM, CPS III, CPS II, Fund III-A, Fund II-A and Fund II-B and each of the Managing Members disclaim beneficial ownership of the securities held directly by Fund III, except to the extent their respective pecuniary interests therein.</footnote>
        <footnote id="F5">These securities are owned directly by Fund III-A.  The Reporting Person, CPSM, CPS III, CPS II, Fund III, Fund II-A, Fund II-B and the Managing Members may be deemed indirect beneficial owners of the securities held directly by Fund III-A as a result of their relationships described in the Remarks (below).  The Reporting Person, CPSM, CPS III, CPS II, Fund III, Fund II-A and Fund II-B and each of the Managing Members disclaim beneficial ownership of the securities held directly by Fund III-A, except to the extent of their respective pecuniary interests therein.</footnote>
    </footnotes>

    <remarks>This Form 4 is being filed jointly by Shane H. Kim, Camden Partners Strategic Manager, LLC (&quot;CPSM&quot;), Camden Partners Strategic III, LLC (&quot;CPS III&quot;), Camden Partners Strategic II, LLC (&quot;CPS II&quot;), Camden Partners Strategic Fund III, LP (&quot;Fund III&quot;), Camden Partners Strategic Fund III-A, LP (&quot;Fund III-A&quot;), Camden Partners Strategic Fund II-A, LP (&quot;Fund II-A&quot;) and Camden Partners Strategic Fund II-B, LP (&quot;Fund II-B&quot;) and Messrs. David L. Warnock, Donald W. Hughes and Richard M. Berkeley (collectively, the &quot;Managing Members&quot; and together with Mr. Kim, CPSM, CPS III, CPS II, Fund III, Fund III-A, Fund II-A and Fund II-B, the &quot;Reporting Persons&quot;). The Managing Members are the managing members of CPS II and CPSM, which is the managing member of CPS III. CPS III is the general partner of Fund III and Fund III-A. CPS II is the general partner of Fund II-A and Fund II-B. Mr. Kim is a director of the Issuer.</remarks>

    <ownerSignature>
        <signatureName>/s/ Shane H. Kim</signatureName>
        <signatureDate>2013-06-17</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ By Camden Partners Strategic Manager, LLC, By Donald W. Hughes, Managing Member</signatureName>
        <signatureDate>2013-06-17</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ By Camden Partners Strategic III, LLC, By Camden Partners Strategic Manager, LLC, By Donald W. Hughes, Managing Member</signatureName>
        <signatureDate>2013-06-17</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ By Camden Partners Strategic II, LLC, By Donald W. Hughes, Managing Member</signatureName>
        <signatureDate>2013-06-17</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ By Camden Partners Strategic Fund III, LP, By Camden Partners Strategic III, LLC, By Camden Partners Strategic Manager, LLC, By Donald W. Hughes, Managing Member</signatureName>
        <signatureDate>2013-06-17</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ By Camden Partners Strategic Fund III-A, LP, By Camden Partners Strategic III, LLC, By Camden Partners Strategic Manager, LLC, By Donald W. Hughes, Managing Member</signatureName>
        <signatureDate>2013-06-17</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ By Camden Partners Strategic Fund II-A, LP, By Camden Partners Strategic II, LLC, By Donald W. Hughes, Managing Member</signatureName>
        <signatureDate>2013-06-17</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ By Camden Partners Strategic Fund II-B, LP, By Camden Partners Strategic II, LLC, By Donald W. Hughes, Managing Member</signatureName>
        <signatureDate>2013-06-17</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Donald W. Hughes, Attorney-in-Fact for David L. Warnock</signatureName>
        <signatureDate>2013-06-17</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Donald W. Hughes</signatureName>
        <signatureDate>2013-06-17</signatureDate>
    </ownerSignature>
</ownershipDocument>
