The House of Commons Speaker's office said May would make the previously unscheduled statement at about 3:30 p.m. (10:30 a.m. EST).
Two further statements from cabinet ministers will follow - one from Brexit Secretary Stephen Barclay and another from Andrea Leadsom, who is in charge of the government's legislative plans.
The meaningful vote requires the draft to be put to both the House of Commons and House of Lords.
And the DUP's Nigel Dodds asked when the prime minister would understand the withdrawal agreement is "unacceptable to this House".
"As a result, if we went ahead tomorrow it would be rejected by a significant margin".
"Why has it taken the prime minister this long to face up to the reality" that lawmakers will not back her deal?
'From listening to those views it is clear that while there is broad support for key aspects of the deal, on one issue, the Northern Ireland backstop, there remains widespread and deep concern. "We can have a withdrawal agreement that does not contain the backstop".
"By contrast, we believe that a no deal situation would be catastrophic for our economy and society".
That is likely to take the form of a statement reassuring MPs that the backstop will never need to be used.
The British government is free to do so as long as no withdrawal agreement has entered force.
But Labour lawmaker Lloyd Russell-Moyle was expelled from Parliament for the day after he grabbed the House of Commons' ceremonial mace as a sign of protest.
"We have known for at least two weeks that Theresa May's worst-of-all-worlds deal was going to be rejected by Parliament because it is damaging for Britain". 'While Theresa May continues to botch Brexit, our public services are at breaking pint and our communities suffer from dire under-investment'.
"Labour's alternative plan for a jobs-first deal must take centre stage in any future talks with Brussels". "Our country deserves better than this", said Mr Corbyn.
It comes amid wide speculation that the Prime Minister could lose the vote by more than 200 votes, a catastrophic loss that would probably have killed off Mrs May's leadership. "This shambles can't go on - so how about it?"
But on Monday, just hours before May's address to Parliament, the EU's highest court ruled that the United Kingdom can cross back if it wants.
Boris Johnson said Mrs May could stay on if she lost Tuesday's vote - but must renegotiate the deal with Brussels. It's the government's "firm policy" that Article 50 will not be revoked, the spokesman said. "This unequivocal and unconditional decision must be communicated in writing to the European Council".
May's Conservative government does not have a majority in the House of Commons, and opposition parties - as well as dozens of Conservative lawmakers - said they would not back the divorce deal.
Chart: Yahoo FinanceMay has received strong backlash over the deal she secured with the European Union - from the Labour opposition, the public, and even inside her own party.
With her own future in the balance, May has repeatedly insisted that her deal, which envisages continued close ties with the European Union, is the only one on the table and that the alternatives are a painful "no-deal" exit from the European Union or possibly no Brexit at all.
Critics say it could leave Britain tied to the European Union indefinitely, unable to strike new trade deals around the world.
Responding to the decision, Leeds East MP and Shadow Justice Secretary Richard Burgon wrote on Twitter: "May's 11th hour decision to cancel the vote on her deal further undermines the Government's credibility".
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