Stuart was injured during the third period of Detroit's 5-4 shootout victory at Calgary on Friday night. He will be sidelined six-to-eight weeks.
The Red Wings are complying with a request by the NHL to supply the league with Stuart's medical information. Stuart's jaw has two displacements but wasn't wired shut.
The hit came in the first full season in which the NHL is handing out discipline for head shots.
"If you make a stand hard enough when this stuff happens, this stuff won't happen," Red Wings coach Mike Babcock said before Detroit played the Vancouver Canucks on Saturday night.
Babcock called the incident "really disappointing" and "a needless play."
"It would have been easier to take his body and not his head," Babcock said. "No reason for it to happen, but that's just my opinion."
Red Wings center Kris Draper called Stuart's absence "a huge loss."
"[League officials] talk about head shots," Draper said. "Well, this is obviously a clear cut one when you break a guy's jaw."
Stuart had been averaging 20 minutes, 57 seconds of ice time per game and is a plus-seven. He plays on special teams and logs regular shifts alongside perennial All-Star defenseman Nicklas Lidstrom.
"No matter what the suspension is, it's not helping us out," Draper said. "That's the thing. We're going to lose Stewie for six, eight weeks, whatever it's going to be.
"That's a huge blow for our hockey club because of the minutes he plays and the quality of minutes that he plays. But the bottom line is, it's got to come to a point where these things have got to stop."
Red Wings general manager Ken Holland expects Kostopoulos to be suspended, but declined to say how long he should sit out.
Kostopoulos could face extra punishment because he is a repeat offender. While playing for Montreal, he was suspended for boarding Toronto's Mike Van Ryn in 2008. Kostopoulos also used his elbow against Minnesota's Nick Schultz, leaving the Wild defenseman with a concussion earlier this season.
Draper wants the NHL to punish Kostopoulos severely to prove that such hit won't be tolerated.
"Hopefully, they get it right this time," he said.