Hjalmarsson was ejected from Monday night's 4-3 win after hitting Buffalo's Jason Pominville from behind just inside the Sabres' zone, sending him flying into the boards, where his head hit the glass violently.
Pominville sustained a concussion and a gash above his eye that required at least seven stitches. He was diagnosed and treated in the building without going to a hospital.
Hjalmarsson was given a five-minute major penalty and a game misconduct, forcing the Blackhawks to play with five defensemen for the rest of the game.
"My intention wasn't to hurt him," Hjalmarsson said after the game. "You never want to see someone laying on the ice like that."
On Tuesday, Sabres goaltender Ryan Miller expressed frustration over the hit.
"I don't even know if there was enough made of it, because Jason was walking out with just stitches," Miller said after practice on Tuesday. "What if Jason has a fractured neck? We don't even know if it's going to have an impact with concussions.
"I just think no matter how badly Hjalmarsson feels, no matter if it's unintentional, we have [to] change the culture of it if we're ever going to change the situations we're seeing where guys are laying [there], guys are bleeding, and missing time with concussions. It's completely an unnecessary play. So I don't think enough's being made of it right now."
The NHL held a hearing with Hjalmarsson Tuesday to determine his punishment. Hjalmarsson will miss Wednesday's game against the Nashville Predators and Friday's game against the Columbus Blue Jackets.
Jesse Rogers covers the Blackhawks for ESPNChicago.com and ESPN 1000. Information from The Associated Press contributed to this report.