The man was dead before he could be taken to hospital, they added.
The incident occurred near Narketpally village around noon when the car driven by Rahim Khan hit Venkat Reddy who was crossing the road.
Reddy was flung onto the roof of the vehicle, but Khan didn't stop.
"The driver continued to drive with the body on the vehicle's roof as far as Kattangoor village, several kilometres further," said deputy superintendent of police Sudhakar.
Passersby alerted the police seeing the body on the top of the car, who stopped it with the help of some local people.
Khan was arrested and booked under section 304A (causing death by negligence) of the IPC. Further probe is on.