Coach Mike Sullivan addressed Bjugstad's status after a morning skate Thursday, prior to the Penguins' 4-3 overtime loss to the New York Islanders.
Sullivan also said that defenseman Justin Schultz will be out "longer term" with a lower-body injury for the Penguins, who have now lost two straight and four of the past five.
Bjugstad joins captain Sidney Crosby as Pittsburgh centers who have undergone core-muscle surgery this season. Crosby had his surgery last Thursday and is expected to be out at least another five weeks.
As the injuries mount -- especially on defense with Schultz and Kris Letang (lower body) out of the lineup -- the Penguins have had to call on reinforcements from AHL affiliate Wilkes-Barre/Scranton. Defensemen Chad Ruhwedel and Zach Trotman, in fact, were recalled Thursday, and both made their season debuts, patrolling the blue line against the Islanders.
"I think we have capable guys, and that's how we look at it," Sullivan said after the loss. "Once again, it's just the adversity, it's the reality of the game, and we're just going to have to learn to deal with it and find ways to win."
The Penguins, at 11-7-4 with 26 points, are 10 behind the front-running Washington Capitals in the Metropolitan Division.
"We believe we've got capable people. We've got a deep organization; we feel as though we've got a deep roster," Sullivan said. "We've got capable guys that we can plug in, and it's a great opportunity for players to step up."
The Associated Press contributed to this report.