The move came shortly after Montreal acquired Dale Weise and Christian Folin from the Philadelphia Flyers in exchange for David Schlemko and Byron Froese.
Alzner has appeared in nine game for the Canadiens in 2018-19, registering one assist. The 30-year-old signed a five-year, $23.125-million contract with Montreal on July 1, 2017.
Philadelphia also made a roster move following the trade, waiving forward Corban Knight. The 28-year-old did not record a point in three games with the Flyers this season.