May said a vote on the deal -- which was postponed on December 11 to avoid defeat -- would be held in the week beginning 14 January.
"This house has no confidence in the prime minister due to her failure to allow the House of Commons to have a meaningful vote," Labour leader Corbyn told lawmakers on Monday ahead of tabling the motion in parliament.
Corbyn said the move was "the only way I can think of ensuring a vote takes place this week".
The government must agree to the non-binding vote and even if successful it would not automatically trigger May's downfall.
House of Commons authorities said the government will decide whether the motion is debated and voted on, but noted it is "parliamentary convention that any such request be granted".
May last week survived a party confidence vote initiated by her own Conservative colleagues opposed to her Brexit strategy, but emerged badly wounded after a third of her parliamentary party voted to oust her.
A vote of no-confidence from a majority in the House of Commons could leave her authority further weakened -- and potentially prompt another vote in her entire government and a general election.
Britain is set to leave the European Union on March 29 next year, but the prime minister is struggling to persuade parliament to accept the divorce deal she struck last month with the bloc after 18 months of tortuous talks.
If parliament fails to approve the text, Britain could crash out of the EU with no deal -- a prospect that experts warn could lead to serious trade disruption and trigger a financial crisis. May insisted Monday that she was continuing to seek "assurances" from the EU over elements of her plan.
However, European Commission spokesman Margaritis Schinas said "no further meetings with the United Kingdom are foreseen".
The delay has angered members of her own party and Labour opposition politicians, who accused her of trying to "run down the clock" ahead of Britain's withdrawal to increase pressure on them to back the deal.
"The prime minister has cynically run down the clock, trying to manoeuvre parliament into a choice between two unacceptable outcomes" -- her deal or no deal, Corbyn said.
"It's... unacceptable that we should be waiting almost a month before we have a meaningful vote on the crucial issue facing the future of this country."
May is again facing more calls for a second referendum to resolve the impasse, with dozens of MPs from all sides now supporting another poll and reports that May's officials are considering the possibility.
But the prime minister has argued vehemently that this would betray the 2016 result and undermine public confidence in politics.
"Let us not break faith with the British people by trying to stage another referendum," she told parliament on Monday.
"Another vote... would do irreparable damage to the integrity of our politics," May said, adding that a second vote "would likely leave us no further forward".
The issue provoked an extraordinary public clash on Sunday between May and former prime minister Tony Blair, a leading supporter of continued EU membership and of holding another poll.
May accused Blair of insulting voters and trying to undermine her government by meeting officials in Brussels.
Blair, who was premier between 1997 and 2007, in turn accused the Conservative leader of being "irresponsible".
But campaigners for a referendum said May's comments on Monday showed that the idea was being taken seriously.
"A new public vote would be different from the referendum in 2016 because we now know more about what Brexit means," said Margaret Beckett, an MP from the main opposition Labour Party and "People's Vote" supporter.
"Any effort to force Brexit over the line without checking that it has the continued consent of the British people will only reinforce divisions," she said.
Another proposal being put forward if May's deal does not pass parliament is for MPs to hold indicative votes on different options to work out what steps to take next.
But May downplayed that prospect, telling lawmakers: "I have no plans for indicative votes".
"What is necessary is for the House to reflect on what members want in terms of their responsibility to come to a decision on this matter.