Stuart was injured during the third period of Detroit's 5-4 shootout victory at Calgary on Friday night. He's expected to be sidelined for at least six weeks.
"Kostopoulos delivered a blow to the head of an unsuspecting and vulnerable player," NHL disciplinarian Colin Campbell said in a statement. "As well, he targeted the head of his opponent and, while the hit was not from the blindside, the head was the principle point of contact."
Campbell also said the fact that Stuart was not in possession of the puck at the time was a factor in his decision.
Kostopoulos and acting Flames general manager Jay Feaster released a statement maintaining the team's position that the hit was legal and thus the suspension unwarranted.
"I'm extremely disappointed in the League's ruling as I believe I have not done anything illegal," said Kostopoulos. "I'm sorry that Brad was hurt on the play and I hope he returns to play soon, but it was never my intention to injure him and I definitely did not target the head."
The Red Wings called for the league to come down hard on Kostopoulos, with Detroit head coach Mike Babcock saying Saturday, "If you make a stand hard enough when this stuff happens, this stuff won't happen."
Babcock also called Kostopoulos' hit "really disappointing" and "a needless play."
Kostopoulos will forfeit US$29,569.92 in salary. The hit came in the first full season in which the NHL is handing out discipline for head shots.
A Kostopoulos elbow also sidelined Minnesota's Nick Schultz with a concussion earlier this season.