The incident occurred early in the second period of Saturday night's game in Columbus as Desjardins was turning up the ice to follow the puck. Byers delivered a shoulder-to-head hit was assessed a five-minute major and a match penalty on the play.
The 25-year-old forward also picked up a second major penalty for fighting Sharks forward Brad Winchester following the hit.
Speaking to reporters after the game, Sharks head coach Todd McLellan was not happy with the type of hit his player received.
"I feel for (Desjardins)," McLellan said. "He's really starting to fit in with our team and getting more penalty-killing time. He's been a very competitive guy and to see him get hit like that, that is exactly what we want to eliminate from the game."
Desjardins had to be helped from the ice by teammates and did not return to the game. He also did not play the following night against the Chicago Blackhawks and no timetable has been set for his return to action.
Byers previously served a one-game suspension while with the New York Rangers for his role in a fight with the Vancouver Canucks in November of 2009.
The Nipawin, Saskatchewan native has yet to register a point in five games this season with the Blue Jackets and has one goal and 55 penalty minutes in his 11-game NHL career.
Byers will forfeit nearly $9,000 in salary.