Reddit users commenting on the video have slammed the driver as a "tosser" and a "mental case".
"That person should LOSE their licence, period," one person wrote.
"86 people have died on the roads already this year. Something has to change," another commented.
A police spokeswoman confirmed this morning they had received a complaint about the car yesterday.
"We are making inquiries to identify the driver," she said.
A spokesman from Snap Vehicles, the rental company that owns the vehicle involved in the incident, labelled the footage "scary".
National Operations Manager Jono Bennett said the company would be helping police with their investigation and helping with attempts to locate the driver.
Bennett also said the company tried to make sure drivers are across New Zealand's road rules and comfortable driving within these.
"When we hand over the car we provide a little pamphlet and show them a video talking about how to drive in New Zealand," he said,
If the drivers were not familiar with the roads Bennett said Snap staffers would encourage them to practise on back roads before heading onto main roads.