Perez, who saved 39 games last season, will not throw for the next week to 10 days. Once he resumes his program, the Indians estimate he will be pitching in games in three or four weeks.
Indians manager Terry Francona said he wasn't sure whether Perez would be OK for opening day.
"I don't know. One thing, we're going to do is take care of it so it's gone and he can pitch effectively. That's kind of an artificial deadline because when he's good to go, that's when he'll pitch,'' Francona said.
"He's down for 10 days and then start his throwing program. We'll see where he's at at the end of spring training. If he is good to go, it obviously effects us nothing,'' he said. "If he's not we'll probably back up Vinnie [Pestano to the closer's role] and back everybody up a little bit. For right now it doesn't change anything in spring training.''
The injury will prevent Perez from playing for the United States in the World Baseball Classic.
It is the second straight spring training Perez has been injured. He strained a muscle in his left side during his first bullpen session on Feb. 23 last year but recovered in time for opening day, when he allowed three runs in the ninth against Toronto in a game the Blue Jays won in 16 innings.
"I'm not saying nothing,'' Perez told reporters Friday as he drove out of Cleveland's spring training complex.
He later tweeted: "Small hurdle at an in-opportune time. I feel better now than I did last year with the oblique. Still plenty of time.''
The right-hander, an All-Star in 2011 and `12, has 98 saves during the past three seasons. Perez was involved in trade rumors during the offseason, but said he's excited about playing for a new manager in Francona.
Cleveland also said right-hander Frank Hermann sprained a ligament in his pitching elbow on Monday against Oakland and outfielder Michael Brantley could return to limited baseball activities next week. Brantley needed 15 stitches to close a cut on his left forearm after he was accidentally spiked Monday by Oakland third baseman Josh Donaldson.