Sussex Police said the vehicle was on routine non-emergency duties when the incident happened at 11.10am in Richmond Place, Brighton.
The 84-year-old man involved in the collision suffered minor injuries, according to police.
He has been taken to the Royal Sussex County Hospital for treatment.
The two officers in the police car were shaken but unhurt, police added.
Anyone who saw what happened can contact Sussex Police at [email protected] or by calling 101, quoting serial 372 of 22/11.
