Toews suffered an upper-body injury in Saturday's 5-2 loss at Nashville.
The 23-year-old ranks second in the NHL with 27 goals and second on the Blackhawks with 50 points in 49 games this season. He also tops the league in both faceoff winning percentage and takeaways.
Pirri, 20, has registered two assists in four games with Chicago this year. He is pacing Rockford with 18 goals and a plus-12 rating and ranks eighth in the AHL with 41 points in 41 contests.