The school announced the suspension Friday night.
Clemson will be without its star wideout for the opener against Auburn in the Georgia Dome on Sept. 1 and the team's first game at Death Valley against Ball State a week later.
Watkins was pulled over during a traffic stop and found to have marijuana and two pills he didn't have a prescription for. He was charged with two counts of possession, both misdemeanor charges. The 19-year-old Watkins was eligible for a pretrial intervention program as a first time offender.
Clemson coach Dabo Swinney had said soon after the arrest Watkins was likely to miss playing time.