Commons Leader Andrea Leadsom indicated the attorney general's full and final advice would be released on Wednesday.
The Government will now be forced to publish Attorney General Geoffrey Cox's full legal advice to the Prime Minister on her deal.
The third defeat came when Tory former minister Dominic Grieve's amendment, which aims to give MPs a greater say should the Brexit deal be defeated on December 11, was approved by 321 votes to 299, majority 22.
Addressing the Commons at the start of a five-day debate on her proposed Brexit agreement, Mrs May said Brexit divisions had become "corrosive" to United Kingdom politics and the public believed the issue had "gone on long enough" and must be resolved.
Labour's shadow Brexit secretary Sir Keir Starmer said that the finding of contempt was "a badge of shame" for the Government, with "huge constitutional and political significance". "It is, I think unprecedented for this House to find government ministers in contempt".
Prime Minister Theresa May speaks in the House of Commons.
A senior European Union legal adviser said on Tuesday Britain had the right to withdraw its Brexit notice, opening a new front in a battle over Prime Minister Theresa May's plans to leave the bloc, which could be rejected in parliament next week.
Bercow said there was an "arguable case that a contempt has been committed", and set aside time on Tuesday to debate the issue - just as members of parliament were meant to begin a five-day debate on Brexit itself before their historic vote on the divorce agreement on December 11.
China, US hail trade truce but key obstacles still remain
President Donald Trump announced in June 2017 that the USA was immediately canceling its participation in the accords. The two were expected to meet Saturday amid a period of increased tensions between China and the United States.
Mrs May's appearance in the Commons on Tuesday will coincide with a presentation at the European Court of Justice, which is hearing a claim by a cross-party group of Scottish MPs, MSPs and MEPs that Westminster politicians could reverse Article 50 - the clause that initiated Brexit - without the consent of the 27 other EU member states.
If her deal falls in the "meaningful vote" next week, the PM has 21 calendar days to set out a statement on her next steps.
This did not refute the allegation of contempt but sought to refer the matter to the privileges committee, which would then produce a report, a process that might have taken weeks.
The row is unlikely to have any impact on the course of Brexit. He added: "Theresa May's majority has evaporated, and the credibility of her deal is evaporating with it".
But the deal still needs to be passed by a majority of British MPs in Parliament.
But May's spokesman told reporters: "It does nothing in any event to change the clear position of the government that Article 50 is not going to be revoked".
She says her deal will maintain close economic ties with the European Union while enabling Britain to trade more freely with the rest of the world and meet voters' demands to reduce immigration.
"I'm focusing on ... getting that vote and getting the vote over the line", she said.
Mrs May said Britain will leave regardless of any future decision by the EU's top court and that the choice is between her deal or no deal.