Nelson, drafted in the fourth round last year out of Southern Mississippi, started 12 games as a rookie for the Bills. He caught 17 passes for 156 yards.
Nelson can practice and play throughout the remainder of the Bills' preseason. The Bills were already short-handed at tight end after Derek Schouman hurt his knee in Thursday's 34-21 preseason victory over the Indianapolis Colts.
Nelson' suspension begins Sept. 4, eight days before the Bills' first regular-season game against the Miami Dolphins.
Nelson will also miss games against the Green Bay Packers, New England Patriots and New York Jets.
Nelson's agent, Joel Segal, declined comment when reached by The Associated Press.
Information from The Associated Press was used in this report.
Fred Jackson of Buffalo Bills needs further testing on handBenzema feeling rejuvenated