Branch, 31, tested positive for marijuana and will reportedly appeal the ban. Four separate positive marijuana tests are required for a player to receive a four-game suspension under the league's policy on the drug.
The suspension will not begin until the appeal is heard, so Branch is eligible to play Sunday at the New York Jets barring team discipline.
Branch was previously suspended by the Patriots in the offseason for violating team rules.
He was arrested in August 2014 for driving under the influence while a member of the Buffalo Bills. The Bills released him shortly afterward and he signed with New England two months later.
Now in his third season with the Patriots, Branch has recorded 33 tackles (19 solo, 14 assists) and one sack in 10 games.