Crosby sustained the injury on Saturday when he was struck in the face with the puck just over a minute into the opening period of the Penguins' 2-0 win over the New York Islanders.
Dr. Bernard Costello performed the surgery on Saturday night, the Penguins said on their website.
Crosby, who has a history of concussions which caused him to miss large parts of the previous two seasons, was injured when team mate Brooks Orpik's slap shot from the point was deflected and struck him.
The NHL's leading scorer was left lying on the ice in a small pool of blood before skating off with the help of Penguins training staff and a towel covering his mouth.
The Penguins are on a 15-game winning streak and two victories shy of matching the NHL record for consecutive wins set by the 1992-1993 Penguins.
Pittsburgh hosts the Buffalo Sabres on Tuesday and then travels to New York on Wednesday to take on the Rangers.
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