Silfverberg was slashed by Cowen midway through the third period of the Ducks' 2-1 victory in Ottawa on Friday night.
The Ducks announced Silfverberg's injury Saturday, saying the Swedish forward will be out 4-6 weeks.
Silfverberg is off to an outstanding start to his first season in Anaheim, with four goals and three assists in his first 11 games. The Ducks acquired Silfverberg in an offseason trade with the Senators for forward Bobby Ryan.
Forward Stefan Noesen, the other Anaheim prospect acquired from Ottawa in the trade, is out for the season with a knee injury.
Anaheim also might face Columbus on Sunday night without center Mathieu Perreault, who sprained his left wrist in Ottawa.
Ducks forward Dustin Penner will rejoin the team in Columbus. Penner has missed the first three games of Anaheim's trip after taking a hard hit last Sunday night from Dallas forward Ryan Garbutt, who was suspended for five games.
After a seven-game winning streak, Anaheim is 1-2 so far on its eight-game trip, its longest of the season.