Bills coach Doug Marrone said after the game that Branch did not dress due to an arrest, but gave no further details.
"It was reported to me that he was arrested," Marrone said in his postgame news conference. "I'm going to meet with him tomorrow. I found out somewhere around noontime, midday. I just had too much on my mind.
"But that's all I know for a fact. I can't say anything else."
Branch, 29, didn't attend Buffalo's offseason voluntary workouts and failed his initial conditioning test at training camp. He didn't appear in the Bills' preseason game against the Pittsburgh Steelers last weekend until the fourth quarter.
An eight-year pro, Branch played his first four seasons with the Arizona Cardinals before moving on to the Seattle Seahawks. He joined the Bills in 2013 and signed a contract extension with the team at the end of last season.
Branch did not attend Saturday's game.
- Ben Estes