Dame Margaret Hodge and Ann Coffey confirmed the move in a letter to the Parliamentary Labour Party chairman.
The motion has no formal constitutional force but calls for a discussion at their next PLP meeting on Monday.
The chairman will decide whether it is debated. If accepted, a secret ballot of Labour MPs could be held on Tuesday.
By early Friday evening, seven other Labour MPs were on record as backing the motion.
Asked if he will resign, Mr Corbyn, who campaigned on the losing Remain side, said: "No, I'm carrying on.
"I'm making the case for unity, I'm making the case of what Labour can offer to Britain, of decent housing for people, of good secure jobs for people, of trade with Europe and of course with other parts of the world.
"Because if we don't get the trade issue right, we've got a real problem in this country," he told Channel 4 News.
By BBC political correspondent Iain Watson
"It may be brutal, it may be bloody, but he has to go. We have no choice."
That's the view of a former Labour minister who's plotting to oust Jeremy Corbyn.
But there was no immediate support from the current frontbench.
Labour's shadow cabinet met for nearly three hours this morning and there were no explicit calls for the leader's resignation.
But there was sustained criticism of the way Jeremy Corbyn had conducted the referendum campaign and what was seen as his failure to address concerns about immigration, and one source insisted: "He was not enjoying the confidence of the room."
Read more from Iain here
Shadow chancellor John McDonnell dismissed the motion of no confidence, saying Mr Corbyn had a mandate to lead the party and predicted that even if Labour MPs forced a fresh leadership election, party members and supporters would back Mr Corbyn again.
Mr Corbyn's critics accused him of being half-hearted in calling for Labour voters to unite behind Remain.
Dame Margaret Hodge said Mr Corbyn should resign because the EU referendum had been a "test of leadership" that he had "failed".
This left Labour voters "not getting a clear message", she added.
Dame Margaret is the MP for Barking and the former chairwoman of the Commons Public Accounts Committee. Ms Coffey is the MP for Stockport.
Mr McDonnell denied that Mr Corbyn was responsible for the vote to leave the EU, and added that a general election looked likely before the end of the year, because a new Conservative leader would want to seek a mandate.
Former shadow chancellor Chris Leslie said there were "failures" in Labour's campaign, saying he would need "an awful lot of persuading to have confidence in Jeremy's leadership into a general election", while former minister Ben Bradshaw said he would support the no confidence motion.
Labour MP Stephen Kinnock has also come out in support of the motion, accusing Mr Corbyn of a "lacklustre" campaign.
However, an online petition on the website of campaign organisation 38 Degrees calling for "a vote of confidence in Jeremy Corbyn after Brexit" has attracted over 90,000 signatures.
And in a joint statement, union leaders have backed Mr Corbyn to continue as leader, saying the "last thing Labour needs is a manufactured leadership row of its own".
They called for Labour to "unite as a source of national stability" and challenge any attempt to use the referendum result to "introduce a more right-wing Conservative government by the backdoor".
In a leaked briefing note, Labour had told its MPs to say the party "best placed" to re-unite the country following the UK's decision to leave the EU.
The briefing note said Mr Corbyn was "uniquely placed" because he understood why many people had voted to leave.
Mr Corbyn won an overwhelming victory in last year's Labour leadership contest, but did not have the backing of most MPs.
The leader was expected to appear at Glastonbury Festival this weekend, but organisers say he has pulled out in the wake of the EU referendum result.
Two Labour MPs have submitted a motion of no confidence in their leader Jeremy Corbyn for failing to give party voters a clear message on the EU referendum.