Faulk was also fined two game checks.
Faulk's suspension began Saturday. He will be eligible to return to the team Sept. 8, the day after New England's opener against Kansas City.
In July, a judge in Lafayette, La., sentenced the 32-year-old Faulk to a year of probation after he pleaded no contest to misdemeanor marijuana charges. Faulk had been issued a misdemeanor summons for possession of marijuana at a Li'l Wayne concert at the Cajundome in February.
Last season, Faulk had 47 catches for 383 yards and one touchdown. He also had 62 rushes for 265 yards.