The Penguins announced Sunday on their official website that Crosby had the surgery after being hit in the mouth with a puck during Saturday's game against the New York Islanders.
However, the team said Crosby is not showing signs of concussion symptoms. No time line has been established yet. Crosby will be re-examined in a few days once swelling goes down.
Crosby also needed dental work after losing several teeth but did not require any wiring in his jaw.
The Penguins announced on their Twitter feed that general manager Ray Shero visited Crosby in the hospital. According to Shero, Crosby "looked pretty good. He was in good spirits."
Crosby missed considerable time the past two years because of concussions. He was sidelined for the final 41 games in 2011 and the Stanley Cup playoffs, in addition to skipping most of the 2012 regular season as symptoms lingered.
"I think every time that type of thing happens to a player you think about it," Penguins coach Dan Bylsma said Saturday.
Pittsburgh, which has won a league-high 15 straight games and is within two wins of the NHL record by Mario Lemieux and the 1992-93 Penguins, hosts Buffalo on Tuesday.
Crosby has enjoyed a resurgence this season, leading the league with 41 assists and 56 points. He holds a 10-point lead over Steven Stamkos in the NHL scoring race.
Saturday's injury could hinder Crosby's march to the scoring title.
A bloodied Crosby, who did not return to the game, skated off the ice with a towel covering his mouth after Brooks Orpik's slap shot from the point deflected off a stick and hit the Canadian center just 1:28 into the game.
"When you see the replay, he had no chance to move," said newly acquired star forward Jarome Iginla, who made his Penguins debut after a blockbuster trade early Thursday morning with the Calgary Flames.
"He didn't see it hit him. It's a very, very unfortunate play."
Crosby immediately fell to the ice and tossed his stick in the air. He then went to the hospital for surgery.
"It's very tough to see that happen to anybody on the ice, but this is your teammate, and Sid's such a great player and a big part of this team," Iginla said.
Information from The Associated Press was used in this report.