"It's a shoulder injury, but I don't know how bad it is," Ducks coach Bruce Boudreau said, according to the team's website. "I assume it's week-to-week. If someone goes out, someone goes in."
Boudreau said Perron isn't expected back with the Ducks before the end of their current road trip, which includes four more games and ends March 28 at Edmonton.
Perron fell awkwardly into the boards early in the second period Sunday against the Winnipeg Jets and did not return to the game, which the Ducks won 3-2.
In 28 games with the Ducks, Perron has eight goals and 20 assists and Anaheim is 21-5-2 since the trade.
Boudreau mentioned Mike Santorelli as a possible replacement for Perron in the lineup.