The NHL-leading Ducks announced the rookie's injury Tuesday. They also recalled goalie Igor Bobkov from the AHL.
Gibson was hurt during warmups before Anaheim's game at Colorado last Saturday. He is 2-2-0 with a 2.28 goals-against average and a .927 save percentage in his first full NHL season.
The 21-year-old Gibson has been the backup to Frederik Andersen, who missed the Ducks' last game with leg tightness.
Anaheim (10-3-0) recalled Jason LaBarbera from its AHL affiliate in Norfolk in time to make 16 saves in the Ducks' 3-2 win at Colorado. Bobkov has never played in the NHL.
Anaheim hosts the New York Islanders on Wednesday.