Sutter has been dealing with a broken jaw, which he suffered on Feb. 9 against the Colorado Avalanche when he was hit by a deflected puck.
The 27-year-old centre struggled to stay healthy in his first season with the Canucks, only playing in 20 games -- scoring five goals and four assists.
Edler also suffered his injury against the Avalanche when he fractured his leg blocking a shot. Edler's injury recovery was originally scheduled to be six weeks.
Vancouver announced on Saturday that Vrbata was out with a lower-body injury.
Edler had six goals and 14 assists in 52 games while Vrbata scored 13 goals and 14 assists in 63 games.