Nathan Zegura, employed by the team as senior media broadcaster, will not work a game until Nov. 25.
Zegura also has been suspended from co-hosting the team-produced Cleveland Browns Daily, a two-hour weekday show on ESPN 850 WKNR. He will not work pregame or postgame shows while suspended.
The team confirmed the actions, which were first reported by Cleveland.com.
Zegura yelled at the official because he did not agree with a pass interference call against Browns cornerback T.J. Carrie in the end zone. The call set up the Saints' first field goal.
Zegura will be replaced by former Ohio State, Eagles and Bills defensive back Dustin Fox.