Two men have been charged by police after footage emerged of a man violently kicking a quokka, one of Western Australia's most loved and iconic marsupials, on Rottnest Island.

The footage shows a young man chasing a quokka around the front yard of accommodation on the holiday island.

He aims a kick at the animal and misses, chases it around a tree and then kicks again, this time connecting.

The quokka is sent flying into a wall.

The quokka is still moving after the impact with the wall, and it is shown desperately trying to flee as the man continues to give chase.

Quokkas' rat-like tails are what inspired Rottnest Island's name. ( Supplied: Peter Murphy )

A man can be heard laughing in the background, while another can be heard saying "come here you little c***".

Police said a 21-year-old man from North Yunderup and a 20-year-old man from Falcon had been charged with cruelty to animals, alleging the incident happened on Sunday evening.

"The men were leaving the island [on Monday] when police located them," a police spokesman said.

"The quokka has not been located and it is unclear whether it was injured. Local authorities will lookout for the animal.

"The men have been evicted off the island."

The men are due to appear in Fremantle Magistrates Court next month.

The safety of quokkas remains a priority, the Rottnest Island Authority says. ( AAP: Adam Gartrell )

Quokkas are found in abundance on the island, and are a major part of its tourist attraction, along with pristine beaches and cycle paths.

However the small marsupial is no longer common on the mainland.

Rottnest Island Authority chief executive Michelle Reynolds said in a statement the safety of quokkas and viability of the population was a priority for the authority.

"Rottnest is one of the last sanctuaries available in the world for this threatened species," she said.

The island got its name from Dutch explorers who dubbed it "Rat's Nest" after landing there in the late 1600s, because of the quokkas' rat-like tails.

Private vehicles are not permitted on the island without a special licence.