The 28-year-old has produced just three goals and three assists in 25 games this year averaging 9:06 of ice time per game.
Downie signed a one-year $1.75-million deal with the Coyotes after scoring 14 goals in 72 games last year with the Pittsburgh Penguins.
The Newmarket, Ont. native was drafted with the 29th pick in the 2005 by the Philadelphia Flyers.
In 433 career NHL games, he's totalled 196 points (76 goals, 120 assists) and 1,057 penalty minutes.