According to Farrell, Peavy, who was scheduled to start Monday in Bradenton, Fla., against the Pirates, cut his finger with a fishing knife Saturday while trying to cut something.
Farrell said it could have been much worse.
"He was at home when it took place and he trying to cut through something, and when it gave way, it almost cut through his finger," Farrell said.
"I don't know how many (stitches). He had a procedure today to make sure there was no infection of any kind and to clean it out. He's idle for the next three days," Farrell said.
Farrell said that Peavy's timetable to start the season may not be affected if he gets back on his throwing program soon. He missed time early when he was hit with a ball and suffered an irritation to his right ring finger. He returned from that with no problem.
Farrell said Peavy, who doesn't have very good eyesight, could be fit with a padding on his glove hand.
Brandon Workman will replace him vs. Pittsburgh.
"This was a freak one," Farrell said. "Honestly, he avoided some serious injury with what took place."