Police said the car was undergoing a forensic examination and fingerprinting.
"Police will be speaking to the parents of the children. No arrests have been made," the statement said.
It is the second such incident in recent months. In June, a car with a toddler and a baby in the back seat was stolen from a Dunedin petrol station.
Their father believed a friend had stayed with his children while he went into the service station.
The thief took the car for a 10km joyride at speeds up to 150km/h before he crashed on Dunedin's southern motorway.
The children, two boys aged 3 and 18 months, were found safe and well.
A 25-year-old Invercargill man is before the court over that incident.