Rinaldo drew a match penalty for punching Girard in the face and setting off a brawl during Colorado's 6-2 victory on Friday.
Just before the punch, Rinaldo delivered a crunching mid-ice hit on Nathan Mackinnon, the Avalanche's scoring leader.
Three game misconducts were handed out as a result of the ensuing brawl: to Mackinnon, Rinaldo and Arizona forward Josh Archibald.
Rinaldo's suspension falls under the category of repeat offender, as the Coyotes center has been suspended four times by the NHL and several times by the AHL.
In 2016, he was simultaneously suspended by both leagues for separate incidents.
Rinaldo, 27, has played 306 career games with the Flyers, Bruins and Coyotes, tallying 30 points and 687 penalty minutes.
He will forfeit $22,580.64 for the latest incident.