Pedroia was hurt rounding first base after his go-ahead, two-run single in the sixth inning of Wednesday night's 5-1 victory over the Orioles and limped off the field.
Boston manager John Farrell announced the decision Thursday and called the four-time All-Star and 2008 AL MVP the "heart and soul of our team."
Pedroia is hitting .306 with nine homers and 33 RBIs.
"The way he plays, what he means in the clubhouse, and what he means on the field with his performance, probably having a career year to date," Farrell said. "Hopefully, this is on the shorter end of time missed. There's no projected date."
Boston demoted struggling right-hander Joe Kelly to Triple-A Pawtucket, where he will make his next start Sunday.
"The options would have been to put him in the bullpen or send him down to start," Farrell said of Kelly. "This centers on command of the baseball. It's certainly not stuff, not athleticism. The frustrating part for Joe and for all involved is when you see an athlete of his ability and it doesn't translate to the consistent command of his pitches."
Kelly is 2-5 with a 5.67 ERA in 14 starts.
Right fielder Jackie Bradley Jr. was recalled from Pawtucket and was batting ninth Thursday. The Red Sox also selected the contracts of right-hander Jonathan Aro and infielder Deven Marrero from Pawtucket.
Catcher Erik Kratz, claimed off waivers from the Kansas City Royals last weekend, was designated for assignment.