Anthony left Tuesday's game against the Cleveland Guardians in the fourth inning after he felt something was wrong following a swinging strikeout.
"Timetable, we don't know," said manager Alex Cora. "Usually it takes from four to six weeks."
Anthony recently signed an eight-year, $130 million contract extension (read more here).
The 21-year-old will be a big loss for a Red Sox team (78-62) that is just 2.5 games back of first place in the American League East division. They currently sit in third behind the first-place Toronto Blue Jays (80-59) and second-place New York Yankees (77-61).
Anthony had been slashing .292/.396/.463 with eight home runs, 32 RBI, and four stolen bases through 71 games. The team will have just 21 games left until playoff time following their Thursday night matchup against the Guardians.
