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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-10-20</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001327567</issuerCik>
        <issuerName>Palo Alto Networks Inc</issuerName>
        <issuerTradingSymbol>PANW</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001468233</rptOwnerCik>
            <rptOwnerName>Arora Nikesh</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O PALO ALTO NETWORKS INC.</rptOwnerStreet1>
            <rptOwnerStreet2>3000 TANNERY WAY</rptOwnerStreet2>
            <rptOwnerCity>SANTA CLARA</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>95054</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>2020-10-20</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>85071</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>533551</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2020-10-20</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F3"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>6950</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>239.28</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>526601</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Each share is represented by a performance-based restricted stock unit (&quot;PSU&quot;). The number of shares reported is at the target award amount.  The actual award earned shall be determined upon certification by the Issuer's Compensation Committee.  If earned, the eligible PSUs from each performance period will vest as follows; Fifteen percent (15%) of the shares shall vest in equal quarterly increments during year two with the first vesting on January 20, 2022; forty-two and a half percent (42.5%) of the shares shall vest in equal quarterly increments during year three; and forty-two and a half percent (42.5%) of the shares shall vest in equal quarterly increments during year four, subject to the Reporting Person continuing to be a Service Provider through each vesting date.</footnote>
        <footnote id="F2">Reflects the forfeiture of previously reported performance stock units granted to the Reporting Person that were eligible to vest based on the certified achievement of certain performance objectives.</footnote>
        <footnote id="F3">This transaction is not a sale of shares by the Reporting Person. Instead, this represents shares that have been withheld by the Issuer to satisfy its income tax and withholding and remittance obligations in connection with the vesting and net settlement of previously reported performance-based restricted stock units.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Rebecca Chavez, Attorney-in-Fact for Nikesh Arora</signatureName>
        <signatureDate>2020-10-20</signatureDate>
    </ownerSignature>
</ownershipDocument>
