The Defence Secretary was one of seven Cabinet Ministers to vote against the Government in opposition to plans to delay Brexit beyond March 29.
Britons voted by 52-48 percent in a 2016 referendum to leave the European Union, a decision that has not only divided the main political parties but also exposed deep rifts in British society.
May is planning to hold another "meaningful vote" on her withdrawal deal by March 20. Lawmakers rejected an attempt to strip her of control over the Brexit agenda.
The Government won the vote on giving Parliament the opportunity to choose another Brexit approach by just two votes, with 16 Tories rebelling against their party. Despite frustration with London, EU leaders have indicated they would accept a "technical extension" of a few weeks if a deal is in the bag.
This raises questions as to whether the amendment will be passed, if it lacks Labour support, and how likely it is such a referendum can be held if it is passed as it requires a deal to be signed off.
"Parliament's rejection of no deal and desire for an extension shows there is still some common sense in Westminster", the influential CBI business lobby tweeted after the vote.
Postponing Brexit gives May some respite, amid a crisis that has shredded her authority and obliterated her control of a fractious Conservative minority government.
It depends in my view on what conditions the European Union places on that extension, because of course the British government now is tasked by parliament to request an extension, and they will undoubtedly provide a time period on that, so they will be asking for an extension for a particular period of time.
The Democratic Unionist party is locked in intensive talks to try to reach an agreement to allow it to back Theresa May's Brexit deal, including with the attorney general, Geoffrey Cox, and the chancellor, Philip Hammond.
Still, she faces a struggle to overturn the huge defeats for the agreement, which was rejected by 230 votes in Parliament in January and by 149 votes this week.
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Asked what she thought of the People's Vote campaign's call for patience, she said: "No one dictates how I vote, except my constituents".
If May's deal is approved, she hopes to use a delay until June 30 to enact legislation needed for Britain's departure.
How long the Brexit delay will last depends-if you can believe it-on how Parliament votes on May's deal a third time.
"We want a deal, we've said we want a deal, and we're talking to them around that", Ms Foster said on Thursday.
Officials and national leaders in the bloc are exasperated at the events in London. The EU rules out reworking the deal May accepted.
In another sting for May, U.S. President Donald Trump said he was "surprised at how badly" the Brexit negotiations have been handled.
She told BBC Radio 4's Political Thinking with Nick Robinson podcast: "The element now is that people will have to take a bad deal rather than no deal".
Article 50 was triggered on March 29, 2017 with the United Kingdom scheduled to leave at 11pm United Kingdom time later March 29, 2019.
The government promised a "strong role" for the now defunct Stormont assembly if the Brexit backstop was triggered, in a document setting out reassurances ahead of the first meaningful vote.
The bloc is more open to a long delay to allow Britain to radically change course - an idea favored by pro-EU British lawmakers who want to maintain close ties with the EU.