The NHL team confirmed the news Tuesday with a posting on Twitter.
Beaulieu, a 22-year-old native of Strathroy, Ont., has one assist in three playoff games. He had one goal and eight assists in 64 regular-season games.
He suffered the injury after taking a hit from Ottawa's Erik Karlsson in the second period of Montreal's 2-1 overtime win on Sunday.
Head coach Michel Therrien said blue-liner Greg Pateryn will replace Beaulieu in the lineup. Pateryn, who was paired with Alexei Emelin at the team's morning practice at Saint-Jovite Arena, did not have a point in 17 games this season.
Montreal can wrap up a four-game sweep with a victory Wednesday night at Ottawa.
The Canadiens also announced Tuesday that they will play a pre-season game against the Pittsburgh Penguins at the Videotron Centre in Quebec City on Sept. 28.