Frank Field, who is backing the Leave campaign, will say the 23 June poll poses "an untold danger" for his party's prospects of power.
The vast majority of Labour MPs back EU membership.
Meanwhile former Labour home secretary Alan Johnson will tell union members that EU membership is "vital" for workers' rights.
The UK's EU vote: All you need to know
Mr Field, the MP for Birkenhead and a former welfare minister, is expected to warn in a speech that the referendum could be "the second-longest suicide note in Labour's history" - behind the manifesto that preceded its 1983 general election drubbing.
Labour leader Jeremy Corbyn, who has expressed Eurosceptic views in the past, recently made his first major speech of the referendum campaign setting out a "socialist" vision for Britain in Europe.
He said there was "nothing half-hearted" about Labour's campaign and said he would continue to make the case for membership in the run-up to polling day.
But Mr Field will say: "The last thing Jeremy needs to do is to undermine further the traditional Labour vote, much of which wishes to leave the European Union.
"For the party leader more actively to campaign for the Remain campaign will push even more Labour voters into the arms of UKIP."
Mr Field, who campaigns for "balanced migration", will criticise an "open-door policy" which he says pushes down wages and puts a strain on public services.
Ahead of the speech, Mr Field said Labour MPs' overwhelming support for staying in the EU was "very unrepresentative" of the views of many of the party's activists in the country at large.
"While the polls show a majority of Labour voters support staying in Europe, about 40% do not and the number of MPs who represent that view are a mere handful," he told BBC Radio 4's Today.
"It is our job to make a good case for leaving Europe so these voters feel that at last their views are being represented in the debate."
The Leave campaign has targeted migration this week with interventions from Michael Gove and Boris Johnson as it attempted to regain the initiative following warnings about the economic effect of a vote to leave.
Alan Johnson, who is leading his party's Remain campaign, will claim a vote to stay in the EU would be as important as the election of Labour's reforming government in 1945, which led to the creation of the NHS and expanded welfare.
"From nurses and builders to railway workers, steel workers, postal workers and shop workers, trade unions will be campaigning for a Britain that remains in Europe," he will tell the Usdaw union's conference.
"The rights of working people are protected by our EU membership, and Labour and our union movement are united in campaigning for Britain to remain in Europe."
Elsewhere in the EU debate, the Commons Foreign Affairs Committee published what it said was a "reliable, unbiased analysis" of the issues involved.
The cross-party committee, which was divided on whether to back EU membership, said it had chosen not to endorse either side.
Instead it urged voters to consider the UK's trading relationship with the rest of the EU and the rest of the world, its "international representation and reputation" and how the EU and its policies might develop in the future.
Committee chairman Crispin Blunt said: "The referendum offers the British people a once-in-a-generation opportunity to chart a course for the UK's role in the world.
"Voters should consider not only the short-term consequences of staying or leaving but the long-term opportunities and challenges."
Labour risks losing "a swathe" of voters to UKIP by campaigning to remain in the EU, one of its MPs is to warn.