Lessio signed with Russian club Medvescak Zagreb on Friday, TSN reports.
Lessio (knee) has been ruled out for the reminder of the 2015-16 campaign, Renaud Lavoie of TVA Sports reports.
Lessio will not be available for Saturday's game against the Rangers, John Lu of TSN Montreal reports.
Lessio scored his first goal of the year Tuesday, snapping a 3-3 tie in the third period to deliver a 4-3 win over Anaheim.
Lessio registered a helper and three hits in Tuesday's 4-3 overtime victory over the Stars.
Lessio returned to action Wednesday night after missing some time with a knee injury and skated 11:21 in a 3-2 loss to the Avalanche.
Lessio (knee) will rejoin the lineup Wednesday against the Avalanche, Arpon Basu of LNH.com reports.
Lessio will travel with the Canadiens for their upcoming three-game road trip.
Lessio (knee) underwent an MRI on Thursday and it's been determined that he will miss 2-to-3 weeks, Renaud Lavoie of TVA Sports reports.
Lessio (knee) won't be in the lineup Wednesday against Buffalo.