A police spokeswoman said the vehicle crashed into a building on the corner of Wansbeck St and Tyne St at 1.23pm today.
No other vehicles were involved.
A St John spokesman said one person was taken by ambulance to Oamaru Hospital with moderate injuries.
A reporter at the scene said the car hit the side of Custom House Gallery and a roundabout sign was down.
A Fire and Emergency New Zealand spokesman said two trucks were sent to the scene and crews assisted with traffic control.