In his second season with the Flyers, Hart has appeared in 32 games and has a 15-11-3 record, a 2.61 goals-against average and .905 save percentage.
Hart had started five of the Flyers' last six games and is 13-2-2 at home, best in the Eastern Conference.
"He did it at practice somehow. He felt a little strain, a little pain and did the smart thing, came off," coach Alain Vigneault said. "We had an MRI and lucky for us, it's not too serious. A couple days, it should settle down. It'll take him to after the [NHL All-Star] break there and he'll be fine after that."
The Flyers have recalled goaltender Alex Lyon from the Lehigh Valley Phantoms of the AHL.
The Flyers are in St. Louis on Wednesday for a game against the Blues.
The team also announced that forward Chris Stewart has been put on waivers.