Kovalchuk, who agreed to a one-year, two-way, $700,000 contract with the Canadiens on Friday, will play his first game since Nov. 9 after practicing on the first line and top power-play unit at the morning skate.
The 36-year-old forward had nine points (three goals, six assists) in 17 games with the Los Angeles Kings this season. He was a healthy scratch in his final 18 games before he was placed on unconditional waivers Dec. 16 and had his contract terminated the next day.
Montreal is looking for its first win in six games (0-4-1) after going 6-2-0 in the previous eight.
Winnipeg is 2-5-2 in its past nine games since going 7-2-1 in the previous 10.