Mrs May will need to secure the votes of 158 of her MPs to stay on as Prime Minister, but will be severely weakened if over 100 vote for her to be ousted.
In a statement, the chairman of the 1922 Committee of Conservative MPs, Sir Graham Brady, said: “The threshold of 15% of the parliamentary party seeking a vote of confidence in the leader of the Conservative Party has been exceeded.
“In accordance with the rules, a ballot will be held between 1800 and 2000 on Wednesday 12th December in Committee Room 14 of the House of Commons.
“The votes will be counted immediately afterwards and an announcement will be made as soon as possible in the evening.”
Owen Paterson became the first former cabinet minister to submit a letter of no confidence on Tuesday, adding to speculation that the threshold might be breached.
However, he said earlier that he did not think his letter had been the one to reach 48.
He told BBC Radio 4’s Today programme: “I saw Graham Brady last night to hand him my letter in person and it appears that my letter did not trigger us over the edge because I think he would have announced it by now.”
Mr Paterson said he had “not found it at all easy” writing his letter, but said: “I just I’m afraid think she’s no longer the right person to lead us through this difficult period.”
He speculated there could be a new PM by mid-January, in the event of a leadership challenge.
If the Prime Minister wins the secret ballot by a simple majority, she cannot be challenged again for a year under Conservative Party rules.
If she is ousted or resigns, a leadership election will see candidates nominated by two MPs, and if more than two candidates put themselves forward, they will be whittled down by ballots of the parliamentary Conservative party every two days until the final two are put to a vote of the party membership.
It is not clear whether the Prime Minister will go ahead with a visit to Dublin planned for today. Mrs May will make a statement this morning in response to the announcement from Mr Brady.
Her cabinet rallied round the Prime Minister, with the Home Secretary Sajid Javid posting on twitter that a leadership election “will be seen as self-indulgent and wrong”.
“The last thing our country needs right now is a Conservative Party leadership election,” Mr Javid said. “PM has my full support and is best person to ensure we leave EU on 29 March”.
Foreign Secretary Jeremy Hunt posted: “I am backing Theresa May tonight. Being PM most difficult job imaginable right now and the last thing the country needs is a damaging and long leadership contest.
“Brexit was never going to be easy but she is the best person to make sure we actually leave the EU on March 29”.
Environment Secretary Michael Gove said: “I am backing the Prime Minister 100% - and I urge every Conservative MP to do the same. She is battling hard for our country and no one is better placed to ensure we deliver on the British people’s decision to leave the EU.”
And the Scottish Secretary David Mundell posted on twitter: “PM has my full support. A leadership contest is the last thing we need. The public want us to sort Brexit now!”