Dame Margaret Hodge submitted a motion, seconded by backbencher Ann Coffey, to the Parliamentary Labour Party, her office said.
It comes as the Labour leader confirmed that he is pulling out of his planned appearance at Glastonbury Festival at the weekend.
Ms Coffey said: “The result of the European Union referendum leaves this country in a mess.
“Leaders have to take responsibility and he has to take his share of responsibility for this, and he should resign.”
She added: “I think, over the weeks, there has been consistent dissatisfaction with him over the referendum campaign, that is not something that is new really, and that dissatisfaction has increased rather than decreased towards the end of the campaign.
“So this motion gives the parliamentary party ... their own right to have a view about his leadership.”
Although the motion has no formal status, it is expected to form the basis of a discussion in the Parliamentary Labour Party about the future of Mr Corbyn’s leadership.
The move means his position now hangs in the balance and it is possible that both the Conservative and Labour Party will hold fresh leadership elections in the coming months.
Ms Coffey, who has been a Labour MP since 1992, acknowledged the no-confidence motion could plunge the party into short-term problems, but said she backed it because she thinks Mr Corbyn cannot lead Labour to victory.
And she said the Remain campaign had been let down by his lack of passion for staying in the EU, which left Labour voters confused about where the party stood
Commenting on the decision to back the motion, she said: “It is something that I would not have done lightly because obviously it is going to create a lot of short-term difficulty, but I just believe that, unless we change our leader, we are not going to win the next election.
“And as we are going to not be part of the European Community, we need more than ever a Labour government that will protect the interests of working people, and that has to be our paramount consideration rather than our loyalty to any particular leader.”
She said: “Westminster has been rocked by a seismic event, the consequences of which are going to be there for probably generations to come.
“And I think, given what has happened, we do need to think very carefully, each of the parties, about the leadership they have been providing in this campaign.”
She said she did not have anyone in mind for leader, but the Labour Party needs to become “more consensual” and to strike up alliances with other parties.
Dame Margaret has asked for the motion to be discussed at the next meeting of the Parliamentary Labour Party on Monday evening with a vote by secret ballot the following day.
Ms Coffey said she doesn’t know how many Labour MPs will vote for the motion, but said she thinks a “sizeable number” support it.
“In a sense, it is not the numbers that matter so much because the motion doesn’t actually mean he has to resign,” she said.
“But he needs to know that a substantial number of the Parliamentary Party have no confidence in his leadership and he needs to consider that and consider whether it is tenable to be leader when his Parliamentary Party does not support him.”
The MP for Stockport said Labour had to rebuild itself after the 1980s and she does not want to see it slide into the electoral wilderness again.
She said: “I saw the slow rebuilding of the Labour Party through the 1980s with the efforts of Neil Kinnock - he built it into a force that then was electable in 1997 with Tony Blair as the leader and that was very hard.
“We have got something hard to rebuild again, but we are running out of time. And if we want to win the next election, we have got to have a leader that the public believe in, not just the party.”