Tuesday's decision, which affirms an earlier High Court ruling, is a setback for Prime Minister Theresa May, who intends to invoke Article 50 of the Lisbon Treaty to leave the bloc by the end of March this year.
The UK's 11 most senior judges voted by eight to three to reject the government's appeal against the earlier ruling.
In his statement, the presiding judge, Lord David Neuberger, said the act of parliament establishing the referendum to leave the EU did not say what should happen as a result.
"Any change in the law to give effect to the referendum must be made in the only way permitted by the UK constitution, namely by an act of parliament," he said.
"To proceed otherwise will be a breach of settled constitutional principles stretching back many centuries."
The ruling means May must put forward legislation to initiate Brexit to MPs for approval, a vote she would almost certainly succeed in passing as the leader of the opposition Labour Party, Jeremy Corbyn, is expected to order his MPs to vote in support of it.
Corbyn reacted to the decision on Monday, saying that his party "respects the result of the referendum and the will of the British people and will not frustrate the process for invoking Article 50".
He also urged the government Brexit plan to include accountability to parliament during exit negotiations as well as a vote on the final deal.
A spokesperson for the government said it would be setting out its next steps shortly but insisted there would be no changes to the current timetable for Brexit.
"The British people voted to leave the EU, and the government will deliver on their verdict; triggering Article 50, as planned, by the end of March. Today’s ruling does nothing to change that," the spokesperson said.
The judgment will not give MPs an opportunity to stop Brexit from happening but will give them more influence on the negotiations, according the University of Surrey’s Simon Usherwood, a specialist on movements that oppose the EU.
"Losing in the Supreme Court isn't going to change the complexity, but it might change the outcome," he told Al Jazeera.
"Despite the broad support for EU membership among MPs, I don't think that will translate into any particular protection of single-market membership, since many MPs will fear that their constituents will see that as trying to get around the referendum result."
Kevin McGuire, associate editor of Daily Mirror, told Al Jazeera that the development was an "emberassment" for May rather than a setback.
"It is embarrasing when Theresa May wanted to act like a monarch and make the decision herself rather than let parliament be sovereign and make the decision," he said. "Brexit will still go ahead."
The court also ruled that the government need not consult devolved parliaments in Scotland, Wales and Northern Ireland.
Scotland's First Minister Nicola Sturgeon expressed disappointment over the court's decision regarding the devolved administrations.
"We are obviously disappointed with the Supreme Court decision in respect to the devolved administrations and the legal enforceability of the Sewel convention," she said in a statement.
The Sewel Convention is a procedure with which a devolved parliament in the UK gives the London government permission to legislate on a devolved matter.
"However, it is becoming clearer by the day that Scotland's voice is simply not being heard or listened to within the UK," Sturgeon said.
"The claims about Scotland being an equal partner are being exposed as nothing more than empty rhetoric," she added.
"This raises fundamental issues above and beyond that of EU membership," she said. "Is Scotland content for our future to be dictated by an increasingly right-wing Westminster Government with just one MP here - or is it better that we take our future into our own hands? It is becoming ever clearer that this is a choice that Scotland must make."
Nicola Sturgeon previously said her administration was not bluffing about a second referendum on Scotland's independence from the UK in case the central government's Brexit negotiations cut her country off from the European single market.
In Northern Ireland, tensions centre on the region's future relationship with the Republic of Ireland, and the potential introduction of a border between the two, a move opposed by most politicians across the sectarian divide.
The British government has struggled to outline its terms for negotiating its exit from the EU after the unexpected vote to leave in June last year.
In opting for a so-called hard Brexit, May’s government faces the prospect of hammering out countless agreements on freedom of movement, trade, and the status of EU and British citizens living in each other's territory.
Earlier this month, the British ambassador to the EU, Ivan Rogers, resigned in opposition to the government’s handling of Brexit, warning it may take up to 10 years to complete.
Once the decision to leave the EU is formally invoked, negotiations between the UK and the EU must conclude within two years.