The 34-year-old forward had surgery after experiencing pain following a 4-3 overtime loss to the New York Islanders on Thursday. It was expected that Bonino would be released from the hospital Saturday.
"He was complaining after the game and we sent him to the hospital just to get things checked out," Penguins coach Mike Sullivan said Saturday before a 5-1 win against the Philadelphia Flyers. "I do think the prognosis is somewhat encouraging, so we'll see where that goes. But we're going to lose him here for a couple of weeks. We have to make sure we take care of business."
Bonino does not have a point in three games with Pittsburgh since being acquired from the San Jose Sharks in a three-team trade March 3.
He previously won the Stanley Cup with the Penguins in 2016 and 2017, mostly playing third-line center. After winning the Stanley Cup for the second time, he signed a four-year contract with the Nashville Predators on July 1, 2017.
"It's hard," Sullivan said. "He's a great guy. He's a real good player. We were all excited to get him involved here for so many reasons. He's a great voice in the locker room. He'll continue to be that for us."
Bonino, who has 19 points (10 goals, nine assists) in 62 games this season, has played fourth-line center since returning to Pittsburgh. Forward Ryan Poehling, who has missed 14 games with an upper-body injury, is an option to replace Bonino once healthy.
"We have [Mikael Granlund], we have [Jeff Carter], we have [Drew O'Connor]," Sullivan said. "'Poehls' isn't ready yet, but he's another guy that would be part of that discussion. We're going to put line combinations together that we think give us the balance we need to give us a chance to win. I'm not going to share them with you."
Forward Alex Nylander was recalled on an emergency basis from Wilkes-Barre/Scranton of the American Hockey League on Friday for the second time in four days. He was called up Tuesday and had an assist in a 5-4 overtime win against the Columbus Blue Jackets before being reassigned Thursday.
"I thought in the game that he played the other night for us, I thought he played extremely well. The forecheck is part of it," Sullivan said. "I think he's a smart player. He has the ability to read plays, anticipate, get to the puck and get to people in a timely fashion because of his recognition skills, his anticipation.
"From what I've seen of his game to this point, I think he has the ability to be good in the pursuit game. We know he has real good playmaking ability."
The Penguins (34-22-10) hold the first wild card into the Stanley Cup Playoffs from the Eastern Conference, two points ahead of the New York Islanders, following a 3-2 overtime win against the New York Rangers on Sunday.
"We've always had a next-man-up mindset in Pittsburgh," Sullivan said. "We believe we have capable people. We have the depth that we need to continue to win games. That's what the expectation is."