Labour leader Jeremy Corbyn has now tabled a vote of no confidence in the government, which could trigger a general election.
The confidence vote is expected to be held at about 1900 GMT on Wednesday.
The defeat is a huge blow for Mrs May, who has spent more than two years hammering out a deal with the EU.
The plan was aimed at bringing about an orderly departure from the EU on 29 March, and setting up a 21-month transition period to negotiate a free trade deal.
The UK is still on course to leave on 29 March but the defeat throws the manner of that departure - and the timing of it - into further doubt.
MPs who want either a further referendum, a softer version of the Brexit proposed by Mrs May, to stop Brexit altogether or to leave without a deal, will ramp up their efforts to get what they want, as a weakened PM offered to listen to their arguments.
Photo source: picture from an open source