Immigration Minister Peter Dutton revealed the 23-year-old would be air-lifted from the Pacific island to hospital in Australia, but made clear that if he survived and recovered he would be sent back.
"I can inform you that there was a 23-year-old male who had originally come from Iran, by boat, was on Nauru and outside of the detention centre, in fact in one of the settlement areas, had set himself alight, self-immolated this morning," he told a press conference.
"He's in a very serious condition and the plan is to provide an air-lift for him later tonight but he is in a very, very serious condition and his outlook is not good at all."
Officials have not said why the man set himself on fire.
Canberra sends asylum-seekers who attempt to enter the country by boat to remote processing centres in Papua New Guinea or Nauru, with no hope of being settled in Australia.
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The policy has been heavily criticised internationally, including by the UN, and in October Nauru's Regional Processing Centre was converted into an "open centre", giving its inhabitants freedom of movement.
It was not clear how long the Iranian had been on Nauru, but Dutton said his self-immolation coincided with a routine visit by a United Nations High Commissioner for Refugees delegation.
The Refugee Action Coalition, an activist group, said four others attempted suicide on Tuesday evening by drinking washing powder and were being treated by medical staff on the island.
"My advice is that there have been other incidents where people have self-harmed or sought to self-harm," Dutton said when asked about the four, while making clear that anyone looking to come to Australia for medical treatment would not be able to stay.
"What we've been very clear about is that if people come to Australia for medical assistance they'll be returning back to Nauru once that medical assistance has been provided," he said.
Three people were returned to Nauru by plane on Wednesday, Dutton added.
"So if people think that through action of self-harm or harming a member of their family that that is going to result in them coming to Australia and staying here permanently, that will not be the outcome."
Canberra has long defended its policy of denying asylum-seekers resettlement in Australia, saying it has prevented deaths at sea and secured the nation's borders. Rights groups have long criticised the policy and conditions in the camps.