Sutter will undergo surgery to fix a sports hernia on his right side. He previously had a similar procedure on his left side in 2015.
The 30-year-old center is expected to miss six to eight weeks.
Sutter hasn't played since Feb. 9. He has six points (four goals, two assists) in 26 contests this season.
The Carolina Hurricanes selected Sutter with the 11th overall pick in the 2007 NHL Draft. The team traded him to the Pittsburgh Penguins on June 22, 2012. After three seasons with the Penguins, the club sent him to the Canucks in a deal that included forward Nick Bonino.
The 11-year NHL veteran has 260 points (135 goals, 125 assists) in 683 career games.
The Canucks (27-30-9) are nine points behind the Minnesota Wild for the second wild-card spot in the Western Conference. Vancouver is 0-2-1 in its last three games entering a matchup against the Toronto Maple Leafs on Wednesday night.