Nicky Morgan has warned that if the next Conservative leader doesn't pursue a deal with the EU, opposition leader Jeremy Corbyn could end up in Downing Street.
The Treasury Select Committee chair said she would be backing Michael Gove in the leadership contest.
"He hasn't completely ruled out no deal, but if we are nearly there on October 31, do we seriously throw our toys out of the pram and walk out?," Ms Morgan told talkRADIO's Julia Hartley-Brewer.
"That will precipitate a vote of no-confidence in the government and that could well herald a general election and Corbyn in Downing Street."
She continued: "Or do you just take that time just to get it right and approved, and avoid all those consequences?".
Environment secretary Gove has said he is open to extending the Brexit deadline by a matter of weeks in order to secure a deal.
"The last thing we need is a Corbyn government, and we don't need a general election either," Ms Morgan continued.
Last night, the leadership candidates were whittled down to 10, after Sam Gyimah failed to secure the backing of eight MPs.
The candidates are: Michael Gove, Matt Hancock, Mark Harper, Jeremy Hunt, Sajid Javid, Boris Johnson, Andrea Leadsom, Esther McVey, Dominic Raab and Rory Stewart.
They will face a vote on Thursday, in which they must secure at least 17 votes to progress in the contest.