Bess, 28, was taken into custody by police at Fort Lauderdale International Airport around 6:19 a.m. ET, the station reported.
It's the second time in as many days that Bess finds himself in the news for all the wrong reasons.
Bess, who capped a disappointing first season with Cleveland by missing the final two games for personal reasons, posted a photo on Thursday morning on his Twitter page of a small package containing what appears to be marijuana. Some of the green-and-brown colored substance is out of the bag and on a table. The photo has since been deleted.
The Browns said the team is aware of the photos and would deal with the situation internally.
Bess was acquired via trade from the Miami Dolphins last April and given a contract extension and $5.75 million in guaranteed money by the Browns. He played in 14 games, then was not seen with the team again. It ended a disappointing season for Bess, who once was named the Dolphins' Man of the Year for his community work.
The Browns said Bess had "personal" reasons for missing the final two games, but shortly after he left the team a photo appeared on his Instagram account that showed him lighting what appeared to be a marijuana cigarette. On Thursday, Bess also had a tweet that also has since been removed in which he referred to African-Americans using the N-word. During the season, Bess had said there never was an appropriate time to use that word.
Information from ESPN.com Browns reporter Pat McManamon and The Associated Press was used in this report.