The goalie was injured in a 2-1 loss to the New York Rangers on Monday.
Bishop, who is 8-5-1 with a 2.33 goals-against average, .923 save percentage and two shutouts this season, made 12 saves and was replaced by Anton Khudobin to start the third period.
"I'm not sure how [Bishop] is but [Khudobin] will get the job done too," Stars center Tyler Seguin said. "We have all the faith in [Khudobin], all the confidence in the world.
Khudobin, who made nine saves, is 3-3-1 with a 2.37 GAA and .925 save percentage.
"It's not easy, but that's the part of the job," Khudobin said. "Not really that I'm planning that I am playing every day, but at the same time I have to prepare for it. Nothing changes."
The Stars (11-8-2) will likely recall goalie Landon Bow from Texas of the American Hockey League before their next game at the Pittsburgh Penguins on Wednesday (7 p.m. ET; ATTSN-PT, FS-SW+, NHL.TV).
"I think [Bishop] and [Khudobin] have put us in the position that we are at right now and our goaltending has been unbelievable all year," Dallas captain Jamie Benn said.
