He is facing charges of exceeding the speed limit after the footage showed him driving at 124km/h (77mph) in a 40km/h (25mph) zone, police say.
The 50-year-old doctor, from Okawa in Fukuoka Prefecture, was reported to police by angry YouTube users.
He reportedly said he “wanted people to understand the beauty of a Ferrari”.
The six-minute video is titled “Ferrari 458 Italia Drive in Japan 2011″ in Japanese, and was filmed using a camera positioned behind the driver.
It shows the car leaving an underground car park and driving along highways and coastal roads in Fukuoka, southern Japan, on the morning of 24 April 2011.
At least 84 people marked dislike under the YouTube posting, compared with 19 likes.
Police said they were tipped off about the video in May and began investigating, the The Mainichi Daily News reports.
According to the newspaper, the police determined the speed of the car based on the distance covered and the time elapsed.
A police spokesman told the AFP news agency that the driver was identified from the footage, and he could face a six month jail sentence or a fine of up to $1,220 (£778) if convicted.