The incident occurred with 2:13 left in regulation of the Lightning's 3-1 home win over the Canadiens on Tuesday. Murray was assessed a match penalty for an illegal check to the head on the play.
Kostka was on the ice for several minutes after the hit. A stretcher was brought out, but Kostka left the ice on his own power.
The Lightning say Kostka has been diagnosed with a concussion.
Murray will forfeit $23,076.93 in salary. He will return for Montreal's second-last regular-season game next Thursday at home to the New York Islanders.
The Canadiens recalled defenceman Nathan Beaulieu from AHL Hamilton. Beaulieu has two assists in 16 NHL games this season.