Ross Township police told WPXI-TV that an officer was searching for a bank robbery suspect Thursday when a black Porsche sped by.
The officer pulled the car over and the driver was identified as Brown, police said.
He was cited for reckless driving.
The Steelers said they're aware of the situation and won't have further comment. A message seeking comment from his publicist wasn't immediately returned.
The Steelers have a game against the Panthers on Thursday night at Heinz Field.
The Panthers have won three games in a row while Pittsburgh has put together four straight wins to take control of the AFC North.