The senior underwent surgery to repair the injury on Wednesday.
Smiley started 11 games for North Carolina this season, tallying 48 total tackles, an interception and a fumble recovery. His 48 tackles rank fifth on the team.
Since moving to the safety position before the 2014 season, Smiley has racked up 100 tackles.
Junior Dominique Green is currently listed as the No. 2 free safety on the North Carolina depth chart.
The Tar Heels (11–1) take on No. 1 Clemson (12–0) in the ACC championship game on Saturday.