The man was hit on a pedestrian crossing in St Michael Street West in West Bromwich.
The police car was responding to a burglary in progress at the time and was said to be driving on blue lights and at low speed.
The incident, which happened around 4pm on Tuesday, saw the man treated by ambulance crews at the scene before being taken to Sandwell Hospital.
He is not thought to have been seriously injured.
A spokeswoman for West Midlands Police said: "A police car on blue lights responding to a burglary in progress hit a man on a pedestrian crossing at low speed on St Michael Street West yesterday around 4pm.
"The man was taken to hospital to be treated for minor injuries."
A spokeswoman for West Midlands Ambulance Service, said: "We were called by the police at 4.19pm to Moor Street, West Bromwich to reports of a road traffic collision involving a car and pedestrian.
"One ambulance attended and treated a pedestrian, a man, who had sustained injuries not believed to be life threatening. He was conveyed to Sandwell Hospital for further checks."