Influential Brexiter Jacob Rees-Mogg submitted the letter to the Conservative 1922 Committee on Thursday, saying the prime minister's deal was "worse than anticipated".
In a tumultuous morning for Mrs May, Brexit Secretary Dominic Raab and Work and Pensions Secretary Esther McVey resigned their posts in acts of defiance.
The prime minister was laughed at in the House of Commons as she insisted she was ensuring a "smooth and orderly" exit from Europe.
A number of junior ministers, including Suella Braverman, Rehman Chishti, Shailesh Vara, Anne-Marie Trevelyan and Ranil Jayawardena, all quit over the deal too.
In his letter to the 1922 Committee, Mr Rees-Mogg, an influential figure in the Brexit-supporting European Research Group, said the withdrawal agreement was "worse than anticipated".
"A few weeks ago, in a conversation with the Chief Whip, I expressed my concern that the Prime Minister, Mrs Theresa May, was losing the confidence of Conservative Members of Parliament and that it would be in the interest of the Party and the country if she were to stand aside," he said.
"I have wanted to avoid the disagreeable nature of a formal Vote of No Confidence with all the ill will that this risks engendering.
"Regrettably, the draft Withdrawal Agreement presented to Parliament today has turned out to be worse than anticipated and fails to meet the promises given to the nation by the Prime Minister, either on her own account or on behalf of us all in the Conservative Party Manifesto."
On the steps of Parliament, Mr Rees-Mogg said that Mrs May's plan "is not Brexit" and "does not meet what we promised our voters".
Watch Theresa May's Commons statement in full
Mrs May had paid tribute to Mr Raab and Ms McVey in the Commons, saying that delivering Brexit involved "difficult choices for all of us".
The prime minister said that the agreed deal offered a "breadth and depth of co-operation beyond anything the EU has agreed with any other country".
"It takes back control of our borders, laws and money. It protects jobs, security and the integrity of the United Kingdom, and it delivers in ways that many said could simply not be done," Mrs May said.
Speaking of the so-called "backstop", she said: "I do not pretend that this has been a comfortable process, or that either we or the EU are entirely happy with some of the arrangements which have been included in it.
"But of course this is the case. This is an arrangement that we have both said we never want to have to use."
In the Commons, Mr Rees-Mogg directly raised the spectre of a leadership challenge to Mrs May.
He had already written to all Tory MPs urging them to vote against the deal.
In the Commons, Jeremy Corbyn described the deal as a "huge and damaging failure".
The Labour leader warned that it did not pass Labour's tests for the party to vote for it.
"The Government is in chaos. Their deal risks leaving the country in an indefinite halfway house without a real say," he said.
"The withdrawal agreement is a leap in the dark - an ill-defined deal by a never-defined date."
Shadow Brexit Secretary Sir Keir Starmer said that Mr Raab's resignation amounted to the prime minister "falling at the first hurdle".
Brexit Secretary Mr Raab, who had only been in the job for a few months after taking over from David Davis, said he could not support the deal "in good conscience".
Tweeting his resignation letter, Mr Raab said: "For my part, I cannot support the proposed deal for two reasons.
"First I believe that the regulatory regime proposed for Northern Ireland presents a very real threat to the integrity of the United Kingdom.
"Second, I cannot support an indefinite backstop arrangement, where the EU holds a veto over our ability to exit."
Ms McVey, the Work and Pensions Secretary, said that the deal put forward "did not honour" the referendum result.
The Tatton MP wrote: "The British people have always been ahead of politicians on this issue, and it will be no good trying to pretend to them that this deal honours the result of the referendum when it is obvious to everyone that it doesn't."
On Wednesday evening, Mrs May said that her Cabinet had "collectively" agreed on the proposed deal.
Mr Vara, a Northern Ireland minister, said that the agreement left the UK in a "halfway house with no time limit on when we will finally be a sovereign nation".
In her statement at No 10, Mrs May said she believed the deal agreed was "the best that could be negotiated".
Speaking at news conference in Brussels he appeared to express hope that Brexit could still be averted.
"The EU is prepared for a final deal with the United Kingdom in November," he said.
"We are also prepared for a no-deal scenario but of course we are best prepared for a no-Brexit scenario."
Responding to Mr Tusk's suggestion that the EU is prepared for a "no Brexit" scenario, Liberal Democrat leader Sir Vince Cable said: "It's good to see that 'no Brexit' is clearly on the table from the EU.
"Any sensible government would be contingency planning for no Brexit, and I am pleased to see that the EU is now planning for it too."