"We're always concerned when one of our players gets a concussion," Sullivan said. "We're concerned for the player, and the nature of concussions as we all know is that they're all very different.
"We're hopeful that Hornqvist can recover as quickly as possible and we can put him back in our lineup. We certainly miss him when he's not in our lineup."
Winger Zach Aston-Reese will be out "longer-term" with an upper-body injury. He left the game after a fight with Florida's Colton Sceviour early in the third period and never returned.
Despite the Pens suffering two player injuries related to fighting (Jamie Oleksiak suffered a concussion after a fight with Washington's Tom Wilson), Sullivan believes fighting is just a part of the game.
"We play a game that's belligerent in nature," Sullivan said. "That's part of the game. These guys are competing hard out there. They're sticking up for one another. I just think it's part of the game."
Neither player practiced on Thursday.