In a corresponding roster move, the Lightning recalled goalie Kristers Gudlevskis from their Syracuse AHL team.
Bishop was hurt in the first period of Tampa Bay's 4-1 win against the Red Wings on Tuesday and did not return.
He was injured while kicking out his right leg to make a pad save on Nick Jensen's shot from along the right boards. Bishop stayed down for a moment before skating gingerly to the bench.
Bishop, an All-Star last season, was re-evaluated Wednesday.
It's a significant loss for the Lightning, who are 16-14-3. Bishop is 9-10-2 with a 2.79 goals-against average.
Information from The Associated Press was used in this report.