Branch was excused from Saturday's 27-14 preseason loss to the Tampa Bay Buccaneers after being arrested for drunken driving in western New York.
State police say Branch was arrested at about 2 a.m. Saturday in the town of Cheektowaga after officers noticed Branch vomiting out the driver's side door of his vehicle.
Police say Branch failed a field sobriety test and had a blood-alcohol content of .14 percent. The legal limit is .08 percent. He was charged with driving while intoxicated and released. He's due back in court on Aug. 29.
Branch, 29, appeared to be battling for a roster spot despite receiving a three-year extension last December and a $3.1 million signing bonus after last season. After starting 13 games last season, Branch played sparingly in the first preseason games, entering in the fourth quarter alongside much less experienced players.
ESPN NFL Insider Adam Schefter and ESPN.com Bills reporter Mike Rodak contributed to this report.