The incident happened on Friday night in Melbourne when the man, who does not want to be identified, splashed petrolon his legs and set himself alight, according to a statement by the Tamil Refugee Council.
He was saved by his housemates, fellow asylum seekers, and was later admitted to an area hospital, news.com.au reported.
"We are very lucky on this occasion that the man's housemates were aware of what he was planning to do otherwise we may have had another death on our hands," council spokesperson Sri Samy said.
The man came to Australia by boat in 2012, and he was on a bridging visa awaiting assessment of his asylum claim. He fled Sri Lanka, leaving his wife and daughter behind, after security police broke his legs.
The council said last week he had learnt his brother, held in a Sri Lankan prison for four years, had disappeared and was feared dead. He feared the same fate if sent to Sri Lanka.
"The previous Labour government, and the current Coalition government, have sent back more than 1000 Tamil asylum-seekers under an enhanced screening process," Samy said.
"That does not allow time for proper assessment of asylum claims." In May, 29-year-old Leo Seemanpillai has set himself ablaze outside his Geelong home while in April a Sydney-based Tamil man was seriously hurt after setting himself alight.
Both were Sri Lankan asylum-seekers, the report said. Sami said the asylum-seekers are fearful of being sent back to Sri Lanka and say "they would prefer to die here than be sent back to torture."
She called on Australian Immigration Minister Scott Morrison to alleviate fear among Tamil asylum seekers by granting protection to genuine refugees.
Most of the Sri Lankan asylum-seekers claim persecution over the Tamil separatist conflict in the country and thus flee to Australia via sea route. Many of them who have attempted to enter Australia illegally have been sent back home.
According to immigration department, over 24,000 asylum-seekers live in Australia on bridging visas.
Australia has a tough refugee policy, according to which asylum-seekers who arrived by boat after July 2013 have been sent to detention centres for processing and permanent resettlement.