Bears general manager Ryan Pace said it is possible White misses the entire 2015 season.
White had missed 11 training camp practices and Chicago's first preseason game prior to Saturday's announcement.
According to the team, White originally sustained a stress fracture in his shin during organized team activities. White then "suffered [a] setback" during practice last week.
On Friday, White told the Chicago Sun-Times, “If it was up to me, I would be out there. I want to be practicing tomorrow.”
The Bears drafted White with the seventh overall pick in the first round of the 2015 NFL draft. He was to be counted on early after Chicago traded Brandon Marshall in the off-season.
In two seasons at West Virginia, White caught 144 passes for 1,954 yards and 15 touchdowns.