The collision happened at the intersection of Granville Street and West 12th Avenue, around 4 a.m. PT.
The impact was powerful enough to deploy one of the car's airbags. The other car was struck on the driver's side rear door.
The B.C. Ambulance Service says three people were taken to hospital in stable condition. The extent of their injuries isn't known. No other vehicles were involved.
Police are investigating to figure out exactly how the two police cars wound up crashing into each other.