Team medical director Dr. Dan Garza evaluated Smith, who was hurt eight days ago against St. Louis.
The 49ers will start second-year quarterback Colin Kaepernick, who replaced Smith in the 24-24 tie with the Rams last week.
Chicago also is without starting quarterback Jay Cutler because of a concussion. Jason Campbell will start.
Smith practiced on a limited basis during the week, but could not pass tests under the NFL's concussion treatment protocol to allow him back on the field against Chicago.
Smith has made 28 consecutive starts and led the 49ers to a 6-2-1 record this season. He was injured during the first half against the Rams and left the game midway through the second quarter.
Last season, his first under coach Jim Harbaugh, Smith led the 49ers to a 13-3 record and within an overtime loss to the Giants of a spot in the Super Bowl.