"He's going to have some X-rays (on his hand), but I think he's going to be out for a little bit," said Stars coach Glen Gulutzan.
Goligoski was injured early in the game when he was hit by a shot off the stick of Penguins forward Chris Kunitz.
"I think it was my second shift of the game," Goligoski said. "Kunitz kind of rolled up high, I was kind of shadowing him out there, and he took a little turnaround shot and the puck kind of got me on the wrong spot on the hand. It happens. It's tough, tough place to do it, too. It's part of the game."
Neal had two goals in the game to seal the win for the Penguins.
Goligoski will fly back to Dallas for the X-rays and will not travel with the team to Detroit for Saturday's game against Red Wings.
Mark Stepneski covers the Stars for ESPNDallas.com.