Senior Sergeant Gillian Meadows said the car and the female cyclist collided at a central city intersection this morning.
Ms Meadows said the crash occured about 8.45am and the cyclist had to be pried out from under the car with help from the Fire Service.
"From my understanding it was standard traffic congestion and it occured at that intersection. At the moment they're still investigating who was in the wrong,'' Ms Meadows said.
The 27-year-old woman was taken to hospital with a broken leg, she said.