Speaking on BBC Radio 4's The World at One, Mr Grieve said his amendment to the bill would not prevent Brexit from happening, but suggested MPs should be able to send the government back to the negotiating table if they did not like the deal that was being put forward.
Mrs May who attempted to reassert authority by sacking Tory vice chair and Brexit rebel Stephen Hammond, could face questions about the vote's implications at a dinner with the other 27 European Union leaders on Thursday, who she will urge to begin trade talks as quickly as possible.
MPs from across different parties voted in favour of Parliament being given a meaningful vote on the terms of Brexit by 309 votes to 305.
Commentators have also warned of domestic trouble ahead for May, as the deal leaves open many questions about Britain's future relationship with the EU. For that reason, Ms May could choose to accept the amendment at the death tonight, rather than lose the vote.
"This amendment has either got to be accepted. or it will be put to a vote", he said.
Dominic Grieve, a Conservative MP and former attorney general, has submitted an amendment to the bill, which has been signed by ten other Tory MPs and is backed by the main opposition Labour party.
Brexit Secretary David Davis has written to Conservative lawmakers, promising the government will not implement a Brexit deal without Parliament's approval.
But ministers want to preserve their special powers - statutory instruments - in the event that this law is not passed in time for Brexit day on March 29, 2019.
Should Parliament vote against the government on any final deal, the Prime Minister could be forced to renegotiate with Brussels - raising the prospect of the United Kingdom crashing out of the bloc without a trade deal and instead being governed by the rules of the World Trade Organization, a course of action sometimes referred to as a "Hard Brexit".
The European Parliament urged EU leaders on Wednesday to allow the next phase of EU negotiations to start, backing a motion that recognised the talks had made sufficient progress as a well a line criticising Britain's Brexit negotiator David Davis.
Gina Miller, a campaigner who successfully fought past year for an increased role for MPs in the Brexit process, said after the vote: "Parliamentary sovereignty wins the day!"
After months of wrangling, May secured a deal last week on three priorities of the separation - Britain's financial settlement, the Irish border and the rights of expatriates.
Grieve had warned that ministers were asking for "a blank check to the government to achieve something that, at the moment, we don't know what it is".
The difference between the Government's position and the demands of the Tory rebels whose votes inflicted the defeat appears small on paper.
Nigel Farage, a long-time member of the European Parliament and a key driving force behind the Brexit campaign, said: "My contempt for career politicians knows no bounds".