Crosby sat out the third period because of a sore hip flexor and Pittsburgh beat the Detroit Red Wings 5-1 on Wednesday night in preseason play.
The injury is not expected to be serious.
"No, not at all," Penguins coach Dan Bylsma said. "Just sore and precautionary, and no need to push it past that."
Crosby said he would not count himself out to play in the team's next preseason game, at Columbus on Friday night, should Bylsma elect to dress him.
"I think I just might have tweaked it a bit," Crosby said. "That's nothing new this time of year for me. It usually takes a couple weeks to get comfortable and feel good. It's noting that I'm too worried about."
Red Wings power forward Johan Franzen left the game with 1:43 remaining in the first period after sustaining a leg injury on a hit by Penguins defenseman Brooks Orpik. Orpik was given a major penalty for kneeing. Franzen missed 55 games last season because of a knee injury.
"We think more of his thigh, but we'll get him checked out," Red Wings coach Mike Babcock said. "We hope he'd going to be fine."
The game was not televised, so no one had seen a replay of the hit, yet players and coaches on both sides reserved comment on whether Orpik should be disciplined. Orpik was not available for comment.
Pittsburgh's Mike Comrie scored the first goal in the new building, connecting at 1:21 of the first period. Ryan Craig had two goals, and Brett Sterling also scored for the Penguins. Ruslan Salei scored for Detroit.
Playing their first home game in Pittsburgh in the 44-year team history at a venue other than the Civic Arena, the Penguins beat the team they had met during two of the past three Stanley Cup Finals.
"The atmosphere was great," Crosby said. "I think all the guys were really excited about being in this game and playing the first one here. It's pretty easy to tell guys came here tonight ready to compete and do a lot of good things."
With a sellout crowd of 18,087 and both teams using much of their "A" lineups, the $321 million arena opened with an almost regular-season intensity.
"It looks like a beautiful building, and I imagine it's state of the art," Babcock said. "Every new building in the league seems to outdo the one previous to it."