Manager Terry Francona said an MRI showed the injury could keep Lugo out for a month to six weeks.
"To put timetables is pretty hard, but ... he got it pretty good," Francona said.
Lugo was injured Friday night while running out an infield single in the ninth inning of Boston's 7-3 loss to the Baltimore Orioles. Lugo began to limp as he approached first base, then dropped to ground shortly after hitting the bag.
The Red Sox on Saturday called up shortstop Jed Lowrie from Pawtucket to replace Lugo. Lowrie was in the lineup for Saturday afternoon's game with Baltimore. Francona said veteran back-up Alex Cora will start Sunday's finale before the All-Star break and the two will split playing time until Lugo returns.
Lowrie hit .310 with a homer and seven RBIs in 17 games with Boston earlier this season. A switch-hitter, he was batting .268 with five homers and 32 RBIs in 53 games with Pawtucket.
"This is one of our young guys that our organization really likes," Francona said. "This will be an opportunity for him to show what he can do, that's for sure, and if he does, good for us. Our organization has had a knack for people being able to fill in. This is another time."
Lugo was hitting .268 with 12 steals for Boston this season.