The news was announced Tuesday on social media by Elite Icons Framing & Memorabilia, where Callahan had been scheduled to attend an autograph signing.
The Bears haven't announced the severity of Callahan's injury, but a source confirmed to ESPN's Dan Graziano that Callahan has a broken foot. There is no timetable for Callahan's return, the source said.
Callahan, the Bears' nickelback, has two interceptions, six passes defended, two sacks and 45 tackles in 13 games (10 starts) this season.
He was replaced in Sunday's game by Sherrick McManis.