The 26-year-old was injured in Tuesday's overtime loss to the Hurricanes. He underwent an MRI on Wednesday.
The Flyers were already without defenseman Justin Braun until after the All-Star break because of a groin injury.
Gostisbehere is a puckmoving defenseman who had 65 points two seasons ago, but he slipped to 37 last season and started out slowly this year. But he has five goals and seven assists in 40 games and has worked on the power play.
The Flyers hold the second wild card in the East, two points ahead of Columbus -- heading into Thursday's games. Philadelphia hosts Tampa Bay Saturday.