The car hit the inspector M Kishtaiah (57) from behind when he was walking.
Mr Kishtaiah died on the spot, inspector of police, Langer House police station, C Anjaiah said.
Mr Kishtaiah was working as a sub-inspector in the special branch of Hyderabad police.
"After the incident, the car driver fled. Some passers-by noted down the car's registration number and based on their information a search has been launched to nab the absconding car driver," the inspector said.
"Unfortunately, today was the SI's marriage anniversary," he said.