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Tim Farron, leader of the fourth biggest party in the House of Commons, made the announcement on Friday morning, making the Liberal Democrats the first party to officially oppose Brexit.
In a statement, Farron said Brits should be given another vote on whether Britain should leave the EU, once May has reached an agreement with European leaders on what a post-Brexit relationship would look like.
In the statement, published on Twitter, Farron said:
"Millions of people are deeply worried about the government's handling of Brexit.
"So my position is very clear: The Liberal Democrats believe that the people are sovereign.
"They must decide whether or not they agree with the deal that the government reaches with Brussels, which means a referendum at the end of negotiations where people can either vote for the deal or remain in Europe.
"We will vote against Article 50 unless it allows the people a vote on the deal, because the will of the people must prevail - both on departure on destination.
"The government has no plan and their haphazard approach is leading us towards a disastrous version of Brexit which risks jobs, communities, security and the economic health of the nation."
Farron campaigned passionately for Remain and has vowed to try and keep Britain in the EU despite the Leave vote. However, the party has just eight MPs in the Commons after its support collapsed in last year's general election, meaning this development probably won't give May much of a headache.
Plus, although a handful of MPs could try to block the Brexit process getting underway, the pressure to respect public will means a majority of MPs will more than likely support the Article 50 bill once it is put to the House.
Another issue with Farron's position is there is no evidence to suggest the public wants a second in-out referendum. Polls published since June 23 suggest British people have no appetite for a second referendum, and even if another vote took place Brits would just vote for Brexit again anyway, according to a recent YouGov survey.
May must secure parliamentary approval before invoking Article 50, after the High Court ruled it would be unlawful for the government to bypass MPs and use royal prerogative to initiate Britain's exit from the 28-nation EU bloc. The government is appealing the decision in the Supreme Court on 5 December.