The Supreme Court's judgement follows an appeal against the High Court's rejection of ministers' arguments.
Theresa May says the government already has powers to invoke Article 50 of the Lisbon Treaty - starting Brexit talks - by the end of March.
But campaigners say Parliament must be consulted before she does so.
Labour has already said it will not vote against the government over invoking Article 50.
The government will learn next Tuesday whether it has won its legal battle to get Brexit under way without the need for a vote by MPs.