A vehicle travelling in the opposite lane had to pull off on to a gravel verge to avoid a head-on collision.
Sgt Brooks said the standard of driving was "shocking", but ''not an unexpected for these roads".
"They are busy [roads] and tourists are trying to reach their destinations in a hurry ... I've stopped people trying to get from Mount Cook to Milford Sound in a day.
"It's pretty hard to change their behaviour because it could be just a one-off visitor.''
Police were grateful to the motorist who filmed the incident and sent it in, he said.
"For them to make that effort, it's great."
Inquiries as to whether or not the driver, who was believed to be Chinese, was still in New Zealand were being made, he said.
Police have contacted Apollo and are locating the driver.