She warned that the challenge to her leadership would endanger the country's exit from the European Union.
A "new leader would have to renegotiate" the Withdrawal Agreement and "one of their first acts would be extending or rescinding Article 50" which would result in "delaying or even stopping Brexit," May said.
That "would only create more divisions just as we need to be standing together."
She added: "I stand ready to finish the job."
The Prime Minister, who was due to travel to Dublin this afternoon to discuss the backstop arrangement, has cancelled her trip. A scheduled Cabinet meeting has also been cancelled.
How was the challenge triggered?
In his statement, Sir Graham Brady, Chairman of the party's 1922 Committee, 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 GMT on Wednesday 12th December," he added.
May has been Prime Minister since July 2016 following the resignation of former Prime Minister David Cameron.
She has been dogged by rumours of a leadership challenge since the 2017 snap elections in which the Conservatives lost their parliamentary majority. Calls for her resignation have grown in the past few months as many within her ranks are dissatisfied with the Brexit deal she secured with EU leaders.
The challenge to the Prime Minister was triggered after at least 48 MPs wrote letters to the 1922 Committee calling for a leadership ballot.
To survive the vote, May needs to get over half of the registered votes cast by the party's 315 MPs. If she wins, no new leadership challenge can be called for a year.
But if she loses, she must resign and a leadership election is then organised.
Several candidates would come forward and a secret ballot would be held within the party with the candidate securing the last amount of votes getting eliminated. The process gets repeated until two candidates remain standing. The vote to determine the winner is then opened to the wider Conservative Party membership.
Who is supporting her?
Cabinet ministers and several high-profile members of the party have come forward to say they would back her tonight.
Foreign Secretary Jeremy Hunt condemned the challenge as "the last thing the country needs."
"Brexit was never going to be easy but she is the best person to make sure we actually leave the EU on March 29," he added.
Environment Minister, Michael Gove, who ran against May in the 2016 leadership contest, said he is "backing the Prime Minister 100%."
"I urge every Conservative MP to do the same," he wrote on Twitter.
Home Secretary Sajid Javid, who is known to have leadership aspirations, and his predecessor Amber Rudd, have also offered their support to the Prime Minister.
Who's against her?
Staunch Brexiteer Jacob Rees-Mogg is the first to have publicly suggested he would vote against her.
"The Country needs a new leader, it is time for Mrs May to resign," he wrote on Twitter.
Rees-Mogg, leader of the eurosceptic European Research Group, is among the 48 MPs to have written to Brady calling for a leadership challenge. In his letter, which was made public, he wrote that "it would be in the interest of the Party and the country if she (May) were to step aside."
Another MP, Simon Clarke, tweeted that he "will vote for change tonight."
Several other leading Brexiteers who have been highly critical of May's approach to the country's exit from the European Union could also oppose her staying in power.
They include former Foreign Secretary Boris Johnson and former Brexit ministers David Davis and Dominic Raab, who all resigned their government positions in protest of May's Brexit strategy.
Can May win?
According to betting company Oddschecker, May is heavily tipped to win tonight's vote.
"Bookies have slashed odds from 1/1 to 1/4 in May's favour of winning the vote. In layman's terms — a 50% chance increase to an 80% chance," the company said in a statement.
Bets on who could win a leadership contest should Theresa May lose the challenge to her leadership tonight, show Johnson, who also ran against May in 2016, in the lead. He is followed by Raab and Javid.
What are the reactions?
The main opposition Labour party's Barry Gardiner, Shadow International Trade Secretary, blasted the Conservative party for "putting the resolution of their own divisions ahead of the interest of the country."
He also told Sky News that Labour ruled out calling for a vote of no confidence on Tuesday, despite May cancelling a crucial vote on the Withdrawal Agreement, for fear of galvanising support for the Prime Minister. He added Labour would look of putting its own motion against the government in the coming days
The centrist Liberal Democrats said the leadership challenge "at this late stage shows what an absolute shambles the Conservatives have made of Brexit."
"It's outrageous, it's embarrassing. Our country's future is at risk because of Tory infighting," the party tweeted.
Nicola Sturgeon, leader of the Scottish National Party described the Conservative Party as a "self-centred bunch."
"This is a stark reminder that the UK is facing chaos and crisis entirely because of a vicious civil war within the Tory Party," she wrote on Twitter.
Donald Tusk, President of the EU council, implied it was business as usual on the continent despite the political turmoil in Britain.
Turk tweeted a picture of a meeting with the EU's top Brexit negotiator, Michel Barnier, ahead of a planned EU leaders summit to be held on Thursday.