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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2016-11-14</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001399529</issuerCik>
        <issuerName>Dicerna Pharmaceuticals Inc</issuerName>
        <issuerTradingSymbol>DRNA</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001259856</rptOwnerCik>
            <rptOwnerName>FAMBROUGH DOUGLAS</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O DICERNA PHARMACEUTICALS, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>87 CAMBRIDGEPARK DRIVE</rptOwnerStreet2>
            <rptOwnerCity>CAMBRIDGE</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02140</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chief Executive Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2016-11-14</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>16600</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>3.78</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>39079</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2016-11-15</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>16500</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>3.63</value>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>55579</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The price reported in Column 4 is a weighted average price. These shares were purchased in multiple transactions at prices ranging from $3.69 to $3.89, inclusive. The reporting person undertakes to provide to the issuer, any security holder of the issuer or the staff of the Securities and Exchange Commission, upon request, full information regarding the number of shares purchased at each separate price within the ranges set forth in footnote (1) to this Form 4.</footnote>
        <footnote id="F2">Includes shares acquired under the DRNA 2014 Employee Stock Purchase Plan in transactions that were exempt under Rule 16b-3(c).</footnote>
        <footnote id="F3">The price reported in Column 4 is a weighted average price. These shares were purchased in multiple transactions at prices ranging from $3.58 to $3.69, inclusive. The reporting person undertakes to provide to the issuer, any security holder of the issuer or the staff of the Securities and Exchange Commission, upon request, full information regarding the number of shares purchased at each separate price within the ranges set forth in footnote (3) to this Form 4.</footnote>
    </footnotes>

    <remarks>Exhibit 24.1 - Power of Attorney</remarks>

    <ownerSignature>
        <signatureName>/s/ John B. Green, attorney-in-fact</signatureName>
        <signatureDate>2016-11-16</signatureDate>
    </ownerSignature>
</ownershipDocument>
