After the game, Oilers coach Jay Woodcroft said he had no further update on Kostin.
The winger was racing to retrieve a loose puck in the offensive zone when he got tangled up with Winnipeg’s David Gustafsson.
Kostin immediately grabbed his knee as Jets defenceman Dylan DeMelo motioned to the Oilers bench for assistance.
Kostin scored Edmonton’s lone goal in the loss.
The Russian has five goals and four assists in 22 games this season.