Officers were patrolling an area in South Hedland in the Pilbara region in northwest Western Australia on Thursday when the crash occurred about 7.40pm.
Police said while on patrol officers felt a bump but believed they had hit the kerb so kept driving.
About a minute later another patrol car saw the injured 45-year-old woman lying on the road at the intersection of Wise Terrace and McLarty Boulevard.
Officers gave the woman first aid and she was taken to hospital with suspected fractures to her legs.
Police say she remains in hospital in a serious but stable condition.
The state’s Major Crash Investigation Unit will now carry out an investigation in South Hedland, which will be overseen by the Internal Affairs Unit.