Shadow Brexit secretary Sir Keir Starmer said: "We have given ministers numerous opportunities to comply with the order of Parliament and to release the Attorney General's full and final legal advice on the Government's Brexit deal".
"This deal.is the best way, I firmly believe, of ensuring that we leave the European Union on March 29", Attorney General Geoffrey Cox told parliament on Monday.
The amendment gives MPs the power to instruct the government what action to take if May's Brexit deal is, as expected, voted down in Parliament.
May is due to address Parliament Wednesday, opening five days of debate before a December 11 vote on the divorce agreement. But the contempt vote demonstrated the fragility of May's government, which does not have a majority in Parliament.
A so-called "meaningful vote" on May's deal will take place in the Commons following parliamentary discussions on December 11.
The Labour Party and others, including the DUP, said that the vote is so important for the future of the country that lawmakers should be able to see any detailed legal warnings concerning parts of the withdrawal agreement.
Following a formal request, Commons Speaker John Bercow said there had been an "arguable case that a contempt has been committed" and ruled MPs should debate the issue on Tuesday, right before the start of five days of debate on the Brexit deal.
Opposition parties and the small Northern Irish party that props up Ms May's minority Government are furious that it only provided an outline of the legal basis for its Brexit deal after Parliament voted to be given the full advice.
In a speech repeatedly interrupted by MPs attacking her deal, the Prime Minister pledged to give Parliament and the devolved administrations a "greater and more formal role" in forthcoming negotiations with the European Union over trade - but declined to say whether MPs would get a vote on that deal.
Downing Street sources attempted to play down the mauling by MPs, insisting that while "everybody knows the parliamentary arithmetic" - the loss of Mrs May's majority as a result of the disastrous 2017 election gamble - the Government had still won the "overwhelming majority" of votes since then.
Advocate General Campos Sanchez-Bordona stated that Britain could halt the entire process without the agreement of other European Union countries. Rejecting it would leave the United Kingdom facing the prospect of a chaotic "no-deal" Brexit, but May's chances of winning majority backing for the deal appear slim.
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".
In the most extreme no-deal scenario, shopping bills could rise by up to 10% but even in an orderly no-deal withdrawal, with a transition period, grocery prices could rise by 6%, he said.
But the deal still needs to be passed by a majority of British MPs in Parliament.
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.