He will join the Canadiens for practice on Thursday in Brossard, Que., before the team travels to Florida to take on the Panthers on Friday.
Montreal also announced that defenceman David Schlemko has been placed on injured reserve retroactive to Dec. 20 due to an upper-body injury.
Alzner was reassigned to the AHL’s Laval Rocket on Nov. 27. He has a goal and an assist with a plus-4 rating in 10 games since then.
He had played eight games for Montreal before being sent to Laval, earning an assist and a plus-2 rating.
Schlemko has played 18 times for the Habs this season, earning a pair of assists, both of them on the power play.