Demers was injured when he collided with Nashville forward Kyle Turris in the third period of Arizona's 2-1 win.
He did not play in a 2-1 loss to the Boston Bruins on Saturday.
Demers had three points (one goal, two assists) in 18 games this season. The 30-year-old has played at least 50 games in all but one of his 10 NHL seasons.
A seventh-round pick (No. 168) in the 2008 NHL Draft by the San Jose Sharks, he has 194 points (44 goals, 150 assists) in 594 games with the Sharks, Dallas Stars, Florida Panthers and Coyotes.
Arizona also is without defenseman Jakob Chychrun (upper body) and Alex Goligoski (lower body), and goalie Antti Raanta (lower body).
