"It is clear that while there is broad support for many of the key aspects of the deal, on one issue, the Northern Ireland backstop, there remains widespread and deep concern," May said.
"We will therefore defer the vote schedule for tomorrow and not proceed to divide the house at this time."
"It is the right deal for Britain, I am determined to do all I can to secure the reassurances this House requires to get this deal over the line and deliver for the British people," May told Parliament.
"I have listened and I have heard concerns...and I will do everything I can to secure further assurances on the backstop."
May held an emergency conference call with her cabinet ministers this morning, amid suggestions that she was to delay the meaningful vote in Parliament on her Brexit deal.
A government source confirmed that the vote was being pulled, with the prime minister due to inform the House of Commons in an oral statement.
The vote was set to be held on Tuesday evening, but the British prime minister appeared to be heading for a certain and heavy defeat which could severely damage her position.
The conference call came after the European Court of Justice ruled that Britain can cancel Brexit without getting the permission of other European Union countries, in a decision that could embolden Remain-supporting MPs to vote down May’s Brexit deal.
A spokeswoman for the court said: "The revocation must be decided following a democratic process in accordance with national constitutional requirements. This unequivocal and unconditional decision must be communicated in writing to the European Council."
Advisers, ministers and loyalist MPs had been urging May to delay Tuesday’s vote in order to seek new assurances from Brussels and avoid the chaos of a parliamentary defeat.
The vote could take place next week or even be delayed until early January, although this would allow less time for the ensuing Brexit legislation to be passed through Parliament before 29 March. The ultimate deadline for the vote is 21 January.