General manager Marc Bergevin said Weber was an easy choice as captain.
"Shea is the perfect guy for the role," he said. "That's the feeling that we got from the players and asking for a vote wouldn't have changed a thing. We wanted a captain to be named before the start of the season."
Forward Brendan Gallagher said if a vote had been held, his would have gone to Weber.
"He's the perfect choice," said Gallagher, who along with forward Paul Byron was named an alternate captain. "Am I disappointed that I wasn't chosen? Absolutely not. … [Weber] had success with his former team in Nashville. He was one of the leaders with Team Canada. He's a role model for kids. When it comes to leadership, he's the definition of it. It's part of who he is."
Weber is unlikely to play this season until December. He had surgery June 19 to repair a meniscus tear in his right knee and was expected to need 5-6 months to recover.
"I hope to return earlier, but if it's another four months, it's another four months," he said during the Canadiens' annual golf tournament at Laval-sur-le-Lac golf club Sept. 10. "I've got to do what's right for myself long term. For me to come back too soon and get hurt again, that doesn't help anybody."
He also had surgery March 13 to repair tendons in his left foot. The foot injury ended his season Dec. 16, after he had 16 points (six goals, 10 assists) in 26 games.
In two seasons with the Canadiens, Weber has 58 points (23 goals, 35 assists) in 104 games.
Selected by the Predators in the second round (No. 49) of the 2003 NHL Draft, Weber has 501 points (189 goals, 312 assists) in 867 games with the Predators and Canadiens. He's scored at least 20 goals three times in 13 seasons, including a personal NHL-high 23 in 2008-09 and 2013-14.
Since the 2005-06 season, Weber's 189 goals are first among defensemen, and his 501 points are fourth, behind Brent Burns (560) of the San Jose Sharks, Duncan Keith (543) of the Chicago Blackhawks and Erik Karlsson (518) of the Sharks.