Murray did not play in Wednesday night's 6-3 loss to the Chicago Blackhawks.
The two-time Stanley Cup winner practiced with his teammates on Tuesday for the first time since going on injured reserve last month. The 24-year-old has struggled this season when able to play. He is 4-5-1 with a 4.08 goals-against average in 11 appearances but declined to use the injury as an excuse for his shaky performance.
"I was playing with it for a few weeks and it was fine," Murray said. "I just tweaked it one day. It didn't hinder many parts of my game. It's a specific place. Just giving it time to heal is the biggest thing."
Murray's next opportunity to return to the lineup will come Friday when the Penguins host the Bruins.
"He is [healthy enough to go], but he's only had one practice," coach Mike Sullivan said after morning skate Wednesday. "So we're trying to get him -- we don't have a lot of practice time. We thought we'd get him a good, solid workout again today and then gauge him over the next couple of games here."
Casey DeSmith started Wednesday against the Blackhawks and gave up four goals on 27 shots.
DeSmith has largely played well in place of Murray. Entering Wednesday, DeSmith was 9-4-4 with a 2.35 goals-against average and a .925 save percentage.
"He's really good," Sullivan said of DeSmith prior to Wednesday's game. "And he's really performed well for us over this last stretch of games."
To make room for Murray, the Penguins sent goalie Tristan Jarry to the AHL.
Information from The Associated Press was used in this report.