Stastny, the team's leading scorer, felt pain in his abdomen Thursday, and the team medical staff determined he needed the appendectomy, trainer Matthew Sokolowski said.
Sokolowski said Stastny is expected to fully recover in two to three weeks.
Stastny would have been the seventh NHL player to follow his father in an All-Star Game.
Stastny has never before missed an NHL game, appearing in all 82 during his rookie season last year and 46 this season.
He has with 17 goals and 32 assists.
The Avalanche recalled center T.J. Hensick from AHL Lake Erie.