This means the government cannot trigger Article 50 of the Lisbon Treaty - beginning formal exit negotiations with the EU - on its own.
Theresa May says the referendum - and existing ministerial powers - mean MPs do not need to vote, but campaigners called this unconstitutional.
The government is appealing, with a further hearing expected next month.
The prime minister's spokeswoman said she would be calling President of the EU Commission Jean-Claude Juncker to say she intended to stick to her March 2017 deadline for triggering Article 50.
Amid suggestions that she might try to call an early general election, she added that Mrs May believed "there shouldn't be an election until 2020 and that remains her view".
A statement is to be made to MPs on Monday but the government says it has no intention of letting the judgement "derail Article 50 or the timetable we have set out"