Higgins, who has eight goals and five assists in 13 games, is scheduled to see a doctor Tuesday to determine how long he will be out of action. He has to wait for swelling to abate for a proper diagnosis to be made.
He will not play against the Edmonton Oilers on Tuesday night.
Higgins suffered the injury in the third period of a 2-1 loss to the New Jersey Devils on Saturday night, but stayed in the game.
In practice on Monday, rookie Guillaume Latendresse was in Higgins' spot on left-wing on a line with Saku Koivu and Michael Ryder.
Centre Alex Kovalev briefly left the game against New Jersey after injuring his right knee, but he is expected to play against Edmonton.