Murray was issued a match penalty with 2:13 remaining in the Lightning's 3-1 home win over Montreal on Tuesday when he elbowed Kostka in the head shortly after the Lightning defenceman passed the puck just inside the Canadiens' blue-line.
Kostka suffered a concussion from the hit and is out indefinitely.
Murray's hearing with the NHL's department of player safety occurred over the phone, meaning the maximum suspension he faced was five games.
The three-game suspension will cost Murray just north of $23,000 US in missed salary.
Here's the NHL's explanation for its ruling:
Murray, who has two assists and no goals in 52 games this season, will sit out Friday at Ottawa (CBC, CBCSports.ca, 7 p.m. ET), Saturday vs. Detroit, and Wednesday at Chicago.
The Canadiens then conclude their regular season with home games against the New York Islanders and Rangers.
Tampa Bay and Montreal currently sit in second and third place, respectively, in the Atlantic Division. Both teams have clinched playoff spots and they are likely to meet in the first round.