Grossman suffered the injury early in the second quarter of an exhibition game in St. Louis when he was knocked down after completing a four-yard pass to Darnell Sanders. He had to be carted off the field and X-rays were taken in the locker room, revealing the ankle break.
This is the second major injury in his brief NFL career. Grossman missed the final 13 games of last season because of a torn ligament in his right knee.
"It's not really going to do me any good to be angry," Grossman said on the team's Web site. "I'm a positive person."
In three games last season, he threw for 607 yards on 47-of-84 passing with one touchdown and three interceptions.
Grossman was Chicago's first-round draft pick in 2003.