Brexit Secretary David Davis, who has been leading negotiations to leave the EU, has resigned from the government.
In his resignation letter, Mr Davis criticised the PM's Brexit plan - agreed by the cabinet on Friday - saying it would leave Parliament with "at best a weak negotiating position".
In her reply, Mrs May said she did not agree but thanked him for his work.
Junior minister Steve Baker quit shortly after Mr Davis - as Mrs May prepares to face MPs and peers later.
In his letter, Mr Davis told Mrs May that "the current trend of policy and tactics" was making it "look less and less likely" that the UK would leave the customs union and single market.
He said he was "unpersuaded" that the government's negotiating approach "will not just lead to further demands for concessions" from Brussels.
Mr Davis, who was appointed Brexit Secretary in 2016, said: "The general direction of policy will leave us in at best a weak negotiating position, and possibly an inescapable one."
In her reply, Mrs May said: "I do not agree with your characterisation of the policy we agreed at cabinet on Friday."
She said she was "sorry" he was leaving but would "like to thank you warmly for everything you have done... to shape our departure from the EU".
Conservative MP Peter Bone hailed the resignation as a "principled and brave decision", adding: "The PM's proposals for a Brexit in name only are not acceptable."
Labour Party chairman Ian Lavery said: "This is absolute chaos and Theresa May has no authority left."
Labour leader Jeremy Corbyn said Mrs May was "incapable of delivering Brexit".
'No choice but resignation'By BBC political editor Laura Kuenssberg
After many months of rumours that he would pull the plug, David Davis has actually quit as Brexit Secretary.
His unhappiness in government has been no secret for some time, but after the prime minister's Chequers agreement with cabinet ministers to pursue closer ties with the EU than he desired, he found his position untenable.
After a visit to Downing Street on Sunday he concluded that he had no choice but to walk.
The move, while not completely surprising, throws doubt on to how secure the government's Brexit strategy is.
In the Commons on Monday Mrs May is expected to tell MPs that the strategy agreed on by the cabinet at Chequers on Friday is the "right Brexit" for Britain.
Brexiteer MP Jacob Rees-Mogg said it would be "very difficult" for Mrs May's plans to win the backing of MPs without Mr Davis.
He told BBC 5 Live: "These proposals will have to come to the House of Commons in legislation and the question is 'will they command support from Conservative MPs?'.
"And I think without David Davis there, without his imprimatur, it will be very difficult for them to get the support of Conservative MPs and therefore the prime minister would be well advised to reconsider them."
BBC political editor Laura Kuenssberg said she understands Mr Davis was "furious" after a meeting at Number 10 earlier on Sunday and "concluded he could not stay in post".
She also said that Environment Secretary Michael Gove is the favourite to take on the vacant post.
On Sunday he told the BBC he was urging Tory MPs to support Mrs May.
Some Remain-supporting politicians said the resignation was evidence of the need for a second referendum.
Lord Adonis, a prominent backer of a second vote, tweeted: "People's Vote to put Brexit out of its misery a big step closer after DD's resignation. Now the Brexiteers holding Mrs May hostage are falling out, there isn't a majority for any withdrawal treaty in Parliament."
The Liberal Democrats called on people to sign a petition for a vote on the proposed deal, adding: "The resignation of David Davis is yet more evidence of the chaos of this Tory Brexit. You deserve the final say".
Conservative MP William Wragg, who campaigned for Brexit, said the resignation was "the right thing to do" while Tory MP Andrea Jenkyns, who quit a junior government role earlier this year to "fight for Brexit", said it was "fantastic news", adding: "Well done David Davis for having the principle and guts to resign".
SNP Westminster leader Ian Blackford called on Mrs May to "see sense and bring forward a plan that heeds the mounting evidence against a hard Brexit".
Nigel Farage congratulated Mr Davis for quitting and called for Mrs May to be replaced as prime minister, accusing her of being "duplicitous" and claiming her response "shows she is controlled by the civil service".