Weber, 32, had seen a number of specialists for the torn tendon in his left foot.
"Following the diagnosis of Shea Weber's injury, it was our belief that after a comprehensive rehabilitation protocol under the guidance of our medical team, Shea would be able to return to play this season," the team's orthopedic surgeon, Dr. Paul Martineau, said in a statement. "Unfortunately, after extensive efforts to heal Shea's injury, progress has not been made as expected."
Martineau said Weber's recovery time will be established after surgery, but the team expects him to be ready for training camp next season.
Weber has missed the past 26 games. He has six goals and 10 assists this season, his lowest output since he played 28 games as a rookie for the Nashville Predators in 2005-06. Weber is in his second season with Montreal after being traded for P.K. Subban.
The Canadiens are stuck in a disappointing season, tied for the second-fewest points in the Eastern Conference and 13 points out of the final wild-card spot.