The 23-year-old Bournival played 29 games with the Canadiens last season with three goals and two assists.
Bournival had three goals and six assists in 12 games with the American Hockey League's Hamilton Bulldogs.
He's played 89 regular-season games in the NHL, all with the Canadiens, scoring 10 goals and adding nine assists. He also played in 14 playoff games.
Bournival was drafted by the Colorado Avalanche in the third round of the 2010 draft. He was acquired by the Canadiens on Nov. 11, 2010, in a trade for defenseman Ryan O'Byrne.