Bosh, Miami's top rebounder and third-leading scorer during the regular season, suffered the injury on a dunk in the Heat's Game One victory over the Indiana Pacers on Sunday after he was fouled by center Roy Hibbert.
An examination on Monday revealed the strain, the Heat said.
Bosh, one of the Heat's "Big Three" along with LeBron James and Dwyane Wade, averaged 18 points and 7.9 rebounds during the 66-game regular season.
He missed nine games during the regular season in which the Heat went 4-5.
The best-of-seven Eastern Conference semi-final resumes on Tuesday in Miami.