In a statement in Downing Street, Mrs May said: "I will contest that vote with everything I have got".
She said a new prime minister would have to scrap or extend Article 50, the mechanism taking Britain out of the EU on 29 March, "delaying or even stopping Brexit".
Conservative MPs will vote between 6pm and 8pm today.
Mrs May said changing Conservative leader would "put our country's future at risk and create uncertainty when we can least afford it".
The challenge to Mrs May's position comes after the required 48 letters calling for a contest were delivered.
Mrs 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.