According to the Herald, Brown was arrested during a trip to his hometown outside of Atlanta after an officer pulled him over for making a lane change without using his blinker. He was released from jail early Saturday morning.
The Dolphins have yet to officially comment on the arrest, but they are aware of the situation, according to the report.
Brown, 28, missed seven games last season after suffering a season-ending Lisfranc injury. A restricted free agent, he is expected to return to the Dolphins after they offered him a first-round tender.
The Associated Press contributed to this report.