Police in Solon (SOH'-lun) say Kosar was arrested early Sunday. A police statement says Kosar was pulled over for speeding at around 2:45 a.m. and officers smelled a strong odour of alcohol.
The police statement says Kosar took sobriety tests and was taken to jail. He was alone in the car.
Kosar didn't immediately return a phone call seeking comment.
The 49-year-old Kosar has publicly talked about how head injuries sustained during his NFL career have affected his speech, making him sometimes slur his words. He has also been addicted to pain medications, gone through a divorce and had financial troubles.