WPXI reports that Brown, who was in a black Porsche, was charged with reckless driving after speeding past an officer.
A Steelers spokesman said the team is aware of the situation and gathering information.
Brown, who had six catches for 96 yards and a touchdown Thursday night against Carolina, departed the locker room after Pittsburgh's 52-21 win and declined comment, telling teammates that reporters were trying to catch him but "they can't catch me."
Quarterback Ben Roethlisberger had a tongue-in-cheek comment about Brown's 53-yard touchdown catch.
"It's one of those ones where I'm going to throw it out there and let AB make the play. He got around (his defender) and he was moving fast," Roethlisberger said.