The quokka, a small marsupial considered an endangered species in Australia, survived the attack.
Thibaud Jean Leon Vallet, 24, and Jean Mickael Batrikian, 18, were each fined A$4,000 ($3,130; £2,080).
In a video taken by Vallet, Batrikian was seen igniting an aerosol spray producing a 30cm (10 inch) flame which singed the quokka's head and body.
The incident caused a public uproar.
The Australian Broadcasting Corporation reported that the two men could not pay the entire fine so were spending one night in jail.
Fairfax Media said the pair were backpackers on a working holiday and had spent three months on Rottnest Island, where quokkas are commonly found. They have since lost their jobs.
The judge called their behaviour "abhorrent" and said the decision to film the act was "perplexing".
"One can only imagine the impact caused to the quokka... Obviously it would have been fearful as a result of what occurred," she said.
Both men pleaded guilty and expressed remorse in court. But Vallet also told Fairfax outside the court: "You think we're monsters. We didn't hurt the quokka. We have pets at home."
The marsupial is also known as the short-tailed wallaby
Quokkas shot to Internet fame earlier this year when the trend of taking "quokka selfies" emerged, where tourists would take pictures with the small cat-sized animals, known to be inquisitive and fearless of humans.
But their curiosity has cost them on occasion.
In the 1990s, a craze of "quokka soccer" - which involved kicking the animals around like a football - broke out on Rottnest Island.
Authorities launched a crackdown and imposed a A$10,000 fine on those caught harming quokkas.
Quokkas are considered an endangered species in Australia
In 2007 a rugby club fined two players for abusing quokkas, and in February this year, five quokkas were found dead and stuffed into tree protectors on Rottnest Island.
The International Union for Conservation of Nature and Natural Resources Red List states that there are between 8,000 to 17,000 quokkas left in the world, most of which are in Australia.