Smith was hurt during a morning practice before Monday night's game against Carolina. Dan Ellis replaced Smith, 10-5-0 with a 3.20 goals-against-average in 17 games this season.
A team spokesman said Smith's injury is considered minor and he is expected to be sidelined approximately two weeks.
Cedrick Desjardins, recalled from Norfolk of the AHL, was Ellis' backup.
Peters came off the bench once - on Dec. 15 at Florida - over the Hurricanes' previous 10 games
Lightning left wing Ryan Malone left Monday's game with an upper-body injury.