Murray exited with 4:21 left in the second period after Philadelphia's Jakub Voracek crashed into him during a breakaway. The 23-year-old managed to skate off under his own power before limping down the runway, clearly favoring his right leg.
Jarry earned his first NHL win against the Lightning Nov. 25, making 33 saves on 35 shots.
"We believe he is a solid goalie," Sullivan said, according to NHL.com. "I think the game he played against Tampa is a perfect example of what he's capable of. Tristan is going to have to make timely saves for us game in and game out. We believe he can do that."
Backup goalie has been a point of concern for the Penguins this season. Antti Niemi, 34, entered the season as the No. 2, but he lasted only three games before being cut loose with a 7.97 goals-against average. That opened the door for the 22-year-old Jarry, who has appeared in only four games this season and one last year.
The Penguins were also missing center Evgeni Malkin Monday for a fourth straight game with an upper-body injury. Sullivan said he is day to day and will accompany the team on its trip to Buffalo Friday.
Information from The Associated Press was used in this report.