Mr Jarvis has previously said he would like to combine the two roles but Labour sources confirmed the National Executive Committee (NEC) agreed at a meeting on Tuesday that MPs should not hold more than one full-time elected public office.
Andy Burnham announced that he would be stepping down as an MP before he wont he Greater Manchester mayoralty last year and a Labour source stressed the NEC was simply formalising an existing convention in the party.
Former soldier Mr Jarvis is currently battling Sheffield councillor Ben Curran for Labour's nomination, which will be announced on Friday ahead of the election itself in May.
Announcing his candidacy in January, Mr Jarvis stressed that he would not take a mayoral salary while continuing in his role as MP.
He argued the Sheffield City Region role was different to other mayoralties as it would have "no power and no resources", insisting he could use a dual role to leverage maximum influence over Yorkshire devolution in Westminster.
He said at the time: "If my first act as Mayor was to stand down as an MP, I’d be needlessly squandering my ability to inflict pressure on the Government through championing our cause in Parliament."
Mr Jarvis also insisted he needed to see through his commitment to serve his constituents in Barnsley, adding: "I take that responsibility extremely seriously and believe that not only is serving the people of Barnsley compatible with serving people across the region, but that the two roles are complimentary – the delivery of better infrastructure and public services will benefit everyone."