Peavy initially injured the ankle while running the bases in his start after rejecting a trade that would have sent him to the White Sox.
Although he pitched with it taped since then, the extent of the injury is worse than originally thought.
"I was getting treatment and we were getting by," said Peavy. "Up until yesterday, I thought it was manageable. It could have gotten ugly if we didn't take the action that we did."
The Padres will start Josh Greer in Peavy's place tonight.
Peavy will wear a walking boot for the next four weeks.
With approximately a month and a half to go until the MLB trade deadline, this likely will end any chance of Peavy, who has a no-trade clause in his contract, getting traded this season.