A fin stabilizer for stabilizing watercraft includes a pivotable stabilizer fin and a receiving space for receiving the stabilizer fin. The stabilizer fin is shiftable from a retracted state in which the stabilizer fin is received in the receiving space to an extended state in which the stabilizer fin extends from the receiving space. Also at least one flexible cover element for at least partially covering an opening of the receiving space, through which opening the stabilizer fin enters and exits the receiving space during retracting and extending, respectively. The stabilizer fin does not contact the at least one cover element when shifting from the retracted state to the extended state.