Sergeant Ben Butterfield, of Dunedin, said details were still very sketchy but it appeared the car the woman was driving down Stuart St about 8.30pm had hit a parked car, opposite the former King Edward Technical College building, and went through a fence into the front yard of a house.
He believed the woman might have attempted to leave the scene.
Alcohol was a possible factor, he said. The woman and the child were under observation at Dunedin Hospital late last night.
Police were continuing to interview witnesses, and asked for anyone who had seen the accident and not spoken to police to call them.