The veteran goaltender, a member of Canada's 2010 Olympic gold medal hockey team, offered no reason for the move but said he would continue to work for the Canucks' goal of winning the Stanley Cup.
"I am honored to have served as captain of the Vancouver Canucks for the past two seasons," the 31-year-old said in a statement.
"Being captain in a Canadian city for a team with such passionate fans is a privilege and an experience I will always take pride in.
"I will continue to be a leader on this team and support my team mates the same way I always have while focusing on our ultimate goal."
The Canucks said they would announce their new "leadership group" before the beginning of the regular season.
"Roberto has been an excellent captain for our team the past two seasons," said general manager Mike Gillis.
"We respect and support his decision to relinquish the captaincy and are confident that he will continue to help lead our team through his tremendous character and work ethic both on and off the ice."
(Writing by Steve Ginsburg in Washington. Editing by Barry Moody)