Crosby was playing with the injury and will need about a week to heal, the team said in a statement released on the eve of all-star weekend.
The reigning Hart Trophy winner will have to miss Pittsburgh's next game, Jan. 27 vs. the Winnipeg Jets, as a result of not playing in the all-star game.
Earlier in the day, the Penguins announced star centre Evgeni Malkin would also miss the all-star game because of injury.
The NHL moved Filip Forsberg up from one of the rookies taking part in the skills competition to the game itself to replace Malkin.
It was not immediately clear who would replace Crosby, who appeared in just one all-star game, back in 2007.