Faried was with two other men in a car stopped at a DWI sobriety checkpoint in Bridgehampton, New York, at about 1:30 a.m. and police said they detected "a strong odor of marijuana emanating from the vehicle."
Faried was charged with fourth-degree possession of marijuana, a misdemeanor for those allegedly in possession of more than 2 ounces of marijuana.
The two other men with Faried, identified by police as Taurean Knuckles, 33, and Atar Hajali, 25, were arrested for unlawful possession of marijuana and given appearance tickets. They were released at the scene.
Faried, 28, was transported to headquarters for processing, police said. He was released on $500 bail.
The Nets acquired Faried in a July trade with the Denver Nuggets. Faried spent his first seven NBA seasons in Denver.
The Nets said in a statement Tuesday that they are aware of the situation involving Faried and "are in the process of gathering more information at this time."
ESPN's Ian Begley contributed to this report.