The NHL-leading Ducks added the veteran Steckel to their roster Saturday before their home game against the Dallas Stars.
Steckel has played in four games for Anaheim this season, spending most of his time with their AHL affiliate in Norfolk. He has played in 423 NHL games for four teams.
Bonino is the Ducks' third-leading scorer with 16 goals and 24 assists while playing in all 56 games during his breakout season.
The centre apparently injured his wrist during the first period of Anaheim's win over Philadelphia on Thursday. He played four shifts in the second period before going back to the dressing room.