May was expected to face a major defeat in the vote, which was scheduled for Tuesday evening in the lower chamber House of Commons.
The move to delay it could provide May with a window of opportunity to go back to Brussels and push for revised terms of departure from the bloc.
But a spokesperson for the European Commission said earlier on Monday the European Union had already offered Britain the “best and only possible” Brexit deal and would not renegotiate a withdrawal agreement.
“Our position has not changed and as far as we’re concerned the United Kingdom is leaving the European Union on the 29th of March, 2019,” spokesperson Mina Andreeva said.
The vote would have seen parliamentarians decide on the EU withdrawal agreement and a declaration on future relations reached by May and European leaders following months of back-and-forth negotiations.
A simple majority was required for approval.
The withdrawal plan includes provisions on citizens’ rights, the transition period, and the so-called backstop arrangement concerning the Irish border, among other issues.
The declaration on a framework for future relations, meanwhile, sets out how the United Kingdom and EU will work together after Brexit in areas such as trade and security.
But scores of May’s ruling Conservative Party MPs were expected to reject her proposal, while several opposition parties, including the main opposition Labour Party, also said they would refuse to back it.
Jonathan Lis, deputy director of the think-tank British Influence, told Al Jazeera that May is in an untenable position.
“It’s a lose-lose situation for the British prime minister because if she does hold the vote then she’ll lose it catastrophically. And if she doesn’t hold it she will have burst all of her authority… What we’re really seeing now is the climax of two years of predictable chaos and ineptitude in parts of the government,” said Lis.
On Monday, Labour Party leader Jeremy Corbyn accused May of continuing to “botch Brexit” in the wake of speculation about the vote on her proposed divorce deal being pulled.
“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,” Corbyn said in a statement posted on Facebook and Twitter.
“Instead, she ploughed ahead when she should have gone back to Brussels to renegotiate or called an election so the public could elect a new government that could do so,” he added.
“We don’t have a functioning government … our public services are at breaking point, 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.”
ECJ ruling, plunging pound
May’s scheduled speech to parliament took place after the European Union’s top court ruled that Britain may unilaterally reverse its decision to leave the bloc.
The European Court of Justice said the UK could revoke Article 50 – the exit clause in the EU’s constitution – “in accordance with its own national constitutional requirements”.
“Such a revocation … would have the effect that the United Kingdom remains in the EU under terms that are unchanged as regards its status as a Member State,” the court said.
Amid the escalating Brexit drama, the UK’s pound sank to its lowest level against the US dollar in 18 months and also fell against the euro.
Market analysts said the plunge was caused by increasing uncertainty and the heightened prospects of a no-deal Brexit.
“There’s so much risk right now, we could certainly see further falls depending on what May can do, or if she falls,” Neil Wilson, chief market analyst at Markets.com, told Al Jazeera.
“Businesses are very worried,” he added.
The UK is due to leave the EU on March 29 next year, two years after it triggered Article 50 and kick-started negotiations with European leaders over a divorce deal.