Anaheim made the move before Saturday night's game at Nashville.
Sutton was hurt in a fight with Detroit's Ruslan Salei during the Ducks' 4-0 loss to the Red Wings on Friday night. The veteran defenseman signed with Anaheim in the offseason.
Festerling was among the Ducks' final cuts of training camp after playing in 42 games for Anaheim last season.
Luca Sbisa is likely to step into the lineup for Sutton, who probably won't play in the final two games of Anaheim's road trip. The Ducks' home opener is Wednesday night against Vancouver.