The challenge to May's leadership was triggered after 48 Conservative Members of Parliament submitted letters demanding a vote to the 1922 Committee, which represents rank-and-file Conservative MPs in the House of Commons.
May, who has been prime minister since shortly after the UK voted to leave the European Union in 2016, has faced criticism in her party for the Brexit plan she has negotiated.
Conservative MPs have triggered a vote of no confidence in 62-year-old May, plunging the Brexit process into chaos as Tory colleagues indicated they no longer had faith in the prime minister to deliver the deal, the Guardian reported.
A ballot will be held on Wednesday evening, Brady said, with votes counted "immediately afterwards and an announcement will be made as soon as possible".
In a press release, he said: "The threshold of 15 per cent of the parliamentary party seeking a vote of confidence in the leader of the Conservative party has been exceeded."
The prime minister will now need the backing of at least 158 Tory MPs to see off the Brexiters' challenge, and her position would then be safe for one year.
The House of Commons has 650 members.
Because the Conservative Party is the largest party in the House of Commons, whoever is leader of the party would be expected to be prime minister.
The vote could hardly have come at a worse time for May, who has been crisscrossing Europe to beg EU leaders for help passing her Brexit deal through the UK Parliament.
May was forced to postpone a vote on the deal on Monday when it became clear she was likely to be defeated in the House of Commons.
Prime Minister May is determined to avoid a no-deal outcome: where the UK leaves the 28-member European Union without transitional arrangements in place.
Businesses have warned it could lead to food shortages, grounded flights and a prolonged economic slump.
If a deal cannot be reached in time, the EU and the UK could agree to extend the March 29 deadline for Britain to leave the 28-member bloc.
The deadlock has led to growing calls for a second referendum on Brexit.
Those calls were buoyed by a decision Monday by the European Court of Justice that the UK can unilaterally revoke Article 50 -- its notification that it plans to leave the EU -- should it so wish.