The Canadiens needed to open a roster spot for Kovalev, who has spent the last seven games on injured reserve. He is to return for a game Monday night against the Toronto Maple Leafs.
Downey has played in only 21 games this season and was a healthy scratch for the last six games. He has one goal, no assists and 48 penalty minutes this season.
Another move will have to be made - possibly sending Andrei Kostitisyn back to AHL Hamilton - if centre Steve Begin is able to play. Begin broke his right foot while blocking a shot Feb. 18 in Columbus.
Coach Guy Carbonneau said a decision would be made before the game whether Begin will play. He has been wearing a protective guard on the foot in practice.
"For sure I can play," Begin said Monday morning. "I've been on vacation enough this season."
He missed 27 games earlier in the season with a sore back.
Also in doubt are forwards Saku Koivu and Sergei Samsonov, who both have a flu. They missed practice on Sunday and also stayed home for the team skate Monday morning, although they may be able to play.
And Josh Gorges, obtained Sunday from the San Jose Sharks with a first-round draft pick for veteran defenceman Craig Rivet, couldn't make it to Montreal because his plane was delayed by weather in New York.
Gorges will meet up with his new teammates on Tuesday when the Canadiens play the Rangers at Madison Square Garden.