Head coach Sean McDermott noted the quarterback was "being evaluated" for the injury, according to Mike Rodak of ESPN.com.
Rodak initially reported that a trainer was holding Anderson's right arm on the way to the locker room.
The injury occurred with just over a minute remaining in the game, as Anderson took a hard sack from Patriots defender Kyle Van Noy. He was helped off the field and was immediately taken to the locker room.
Nathan Peterman took over for the last two plays in the 25-6 loss.
If the injury turns out to be serious, Peterman would be the only healthy player on the roster at the position, as rookie quarterback Josh Allen remains out with a sprained elbow. Considering Peterman has nine interceptions and just three touchdowns in seven career appearances, he isn't a promising option for Buffalo.
Anderson hasn't been much better with zero touchdowns and four interceptions in two games this season, but at least he brings 13 years of NFL experience to an otherwise young roster.