David Davis also said he was "pretty sure" Britain could reach a satisfactory deal with the European Union, and that no deal would be better than a "punishment deal."
When asked by the BBC's Andrew Marr whether May's ouster would be catastrophic, Davis replied "Yes. Yes.
"I happen to think we have got a very good Prime Minister," he said. "I know she is coming under a lot of pressure at the moment, but I have seen her in action. She's bold. She takes her time."
She faces her first major test next week when MPs vote on her legislative agenda, traditionally seen as a test of confidence in the government.
Davis has been mentioned as a potential replacement, but when asked by Marr if he was a leader-in-waiting, he replied: "I'm not getting into it."
The minister, who kicked off talks with his EU counterparts this week, said he was still "pretty sure" of reaching an agreement despite the government's precarious position.
Davis also said Britain would likely need transitional trade arrangements with the EU for up to two years after Brexit.
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