Police in Australia are investigating after a video of a social media personality parading naked around Melbourne's central business district was uploaded to YouTube.

The video of US national Gabi Grecko, who was sporting bunny ears, a green wig, high heels and a wedding veil, has since been taken down, according to Australia's Nine News yesterday.

The stunt was apparently carried out in collaboration with Sneaky magazine, although Nine News said it is not known yet when the footage was filmed.

Nine News says Victoria police are examining whether the stunt warrants a penalty for offensive or wilful and obscene behaviour and are seeking information on when the recording was made.

It added that she could face charges that carry a maximum jail term of two years.

Grecko, 25, was seen by unsuspecting pedestrians including children when she took to Melbourne's aptly named Exhibition Street, according to Britain's Daily Mail.

Shocked pedestrians are caught gawking at the model, while others whip out their smartphones to take a more permanent reminder.

At one point, sirens can be heard blaring in the background, but Grecko appears to escape unnoticed saying: "Woo, we haven't got arrested yet!"

She is seen dancing outside of a restaurant while appalled diners look on, and later meanders into a fast-food joint. Brushing past lines of customers she looks up at the menus above the counter before deciding, "it's too unhealthy," says the Mail.

Appearing on Nine News after footage of the spectacle was uploaded to YouTube, the fiancee of Australian businessman Geoffrey Edelsten, 71, said she didn't mean to "upset" the police.

"I don't want to upset the Australian law enforcement I really have respect for them," she explained.

"To me it's fashion, to me it's art - to other people I'm naked on the street. I'm not ashamed of my body and I'm confident."

According to Nine News, Grecko's fiance was unhappy about the stunt, but was unable to talk her out of it.

The Mail added that the eccentric social media personality recently had her Instagram account closed after she posted a series of topless photos in breach of the platform's no nudity or partial nudity policy.