Jo Johnson resigned as transport minister and invited the public to tell the truth about Brexit.
The deputy, who is the brother of Boris Johnson, said that the withdrawal agreement negotiated with the European Union "will be a terrible mistake".
Claiming Britain was "on the edge of the biggest crisis" since World War II, he said that what was on offer was not "something like what was promised".
Downing Street thanked him for his work but ruled out another referendum.
Jo Johnson voted to stay in the EU in the 2016 referendum, while his brother Boris, who left the foreign secretary in July, was an important brexiteer.
His brother praised his decision, saying they were "united in dismay" by the Prime Minister's negotiation negotiations.
Cabinet ministers were invited this week to read the draft agreement on UK withdrawal with the EU. Theresa May stated that the withdrawal agreement was 95%, but there is still no agreement on how to ensure the absence of hard borders in Northern Ireland.
On Friday, the DUP, whose support Theresa May relies on votes in the House of Commons, has stated that she can not support any agreement that includes the possibility that Northern Ireland will be treated differently from the rest of the United Kingdom.
Mr. Johnson, a deputy from Orpington in Kent, said that the final choice was:
- an agreement that would leave the United Kingdom "economically weakened without saying in the EU rules it must follow", or
- a "no-deal Brexit" that "inflicts non-quantified damage to our nation".
He described this as "a failure of British politics not seen by the Suez crisis", but said that even a Brexit without agreement "could be better than the endless purgatory" proposed by the prime minister.
But in a warning to his brother and his fellow Brexiteers, he added: "To inflict such serious economic and political damage on the country will leave an indelible impression of incompetence in the public mind".
The "democratic thing to do is give the public the last word," he said.
Analysis of BBC political director Laura Kuenssberg
For some time, Jo Johnson has struggled with the evolving reality of Brexit.
A respected and respected member of the government decided that what was promised to the people during the referendum campaign is now so different from what is on the table that the government has left.
He is not the first, nor the best-known minister, to resign for Brexit. But starting right now, just when Theresa May is trying to mend a final deal, could have a serious impact.
Read Laura's complete blog
He added: "It's not about re-doing the 2016 referendum, but asking people if they want to go ahead with Brexit now that we know the agreement that is actually available to us, if we should leave without any agreement or if people in balance they would prefer to keep the agreement we already have in the European Union.
"Britain is on the edge of the biggest crisis since the Second World War. My loyalty to the party is imperfect. I have never rebelled against any problem before now.
"But my duty towards my constituents and our great nation forced me to act".
& # 39; Lost Authority & # 39;
In response, a Downing Street spokesman said: "The 2016 referendum was the biggest democratic exercise in the history of this country and we will not under any circumstances have a second referendum.
"The Prime Minister thanks Jo Johnson for his work in the government".
Mr. Johnson is the sixth minister of Theresa May's government to resign specifically to Brexit, following David Davis, Boris Johnson, Philip Lee, Steve Baker and Guto Bebb.
For the job, the shadowy Brexit minister Jenny Chapman said that Ms. May has "lost all authority and is unable to negotiate a Brexit agreement within her own party, let alone with the EU".
In an interview with the German magazine Der Spiegel, however, he asked if he would stop the Brexit if he had the chance, Jeremy Corbyn replied: "We can not stop it, the referendum took place."
Lib Dem's leader, Sir Vince Cable, whose party supports the demand for a "People & # 39; s Vote" in the final agreement, said: "We warmly welcome Jo Johnson's support for the campaign to give people the last word on the agreement and the chance to leave Brexit.
"This is a fascinating situation in which Jo and his sister are united in opposing their brother Boris and his plans on Brexit".
MP of Brexiteer Tory Andrea Jenkyns tweeted that he did not agree with him on another referendum – but his speech highlighted an unease on both sides of the debate, with the Prime Minister's efforts to secure an agreement.
And conservative pro-conservative Anna Soubry supported her decision and said it was time for another referendum.
David Davis, who left the role of Brexit secretary for Ms. May's Checkers Brexit plan, tweeted: