Lawrence and Walker are starting cornerbacks, while Stewart and Miles are top backups in the secondary.
Notice of the suspensions comes one day after Yahoo Sports reported that UNC is investigating a hazing incident among members of the football team.
The school announced in June that the NCAA has re-opened its investigation into alleged academic fraud involving Tar Heels football and men's basketball players.
The Tar Heels went 7-6 in 2013 and open the upcoming season Saturday at home against Liberty.
- Chris Johnson