The Ducks announced Palmieri's injury Friday, saying he hopes to return for Anaheim's final preseason game.
Palmieri set career highs with 14 goals and 17 assists in 71 games last season.
He has spent parts of the last four seasons in Anaheim, recording 29 goals and 31 assists. Palmieri also has scored three goals in each of the last two postseasons.
Ducks prospect Shea Theodore also will be out at least for a month after spraining a ligament in his right elbow last weekend. The defenseman was Anaheim's first-round pick in 2013.