"Approximately two minutes later the driver has crossed the centre line, crashed and rolled their vehicle off the road," the statement said.
"Ambulance has been called to the scene, however the road is not currently blocked."
A driver who had passed by the crash said it occurred just south of the 70km zone in Herbert. She believed the car had gone down a bank.
Southern fire communications shift manager Mau Barbara said fire services were called at 4.27pm by police. The person had been freed from their vehicle, he said.
The Serious Crash Unit has been notified, and the Independent Police Conduct Authority will be advised, police said.
Anyone who saw the crash or the driver is asked to contact Oamaru Police on (03) 433 1400.