They say the woman in her 50s was hit by a white van while crossing Marshlands Rd at the intersection with Voss St in the suburb of Shirley, about 8.20pm yesterday.
She was knocked to the ground and was bleeding from her head.
The driver didn't stop to help the woman, who was taken to hospital with serious injuries, police said.
She is now in a stable condition.
Police say the van had pipes along its roof and will be missing a wing mirror, which was found at the scene.
Anyone with information is asked to contact police via 105 and quote file number 220813/5063.