A 30-year-old Chinese man, visiting Queenstown with his female partner, were in the Nissan Tiida, which he attempted to drive from its overnight parked position in Malaghan St, Queenstown Hill, at 11am.
''If it hadn't been Waitangi Day, it could have had dire consequences,'' Sergeant Blair Duffy, of Queenstown, said.
It appeared the driver stepped on the accelerator pedal instead of the brake.
The car, with the tourists inside, travelled down the hill, across the intersection with Henry St and a vacant driveway before crashing through the playcentre's wooden fence and coming to a halt with the front wheels hanging over a bank.
The car stopped about 1m from a playhouse.
Sgt Duffy said the driver appeared to be at fault.
The cause was not mechanical, he said. Police issued the man with an infringement notice, with a fine of $600, and he was forbidden to drive until he departed New Zealand on Tuesday.
The tourists were not injured and their rental car had insurance cover.
Playcentre supervisor Marata Cooney, of Arthurs Point, was relieved it happened on a holiday and that no-one was hurt.