The 23-year-old Iranian, known only by his first name Omid, was airlifted to Brisbane on Thursday with third-degree burns to most of his torso.
In a statement, Dutton said that “appropriate support” was being provided to his wife and friends of the man.
“The man was taken to Republic of Nauru Hospital for medical treatment by the Nauruan authorities. He was then transferred to Australia by air ambulance for medical treatment,” Dutton said.
“The man passed away this afternoon in a Brisbane hospital. The department expresses its sympathies to his wife, family and friends.”
The death will be reported to the Queensland coroner.
Omid set himself on fire outside the Nauru detention centre on Tuesday.
The incident coincided with a visit from three Canberra-based UNHCR staff, who all witnessed the man’s actions.
The ABC understands the man has been on Nauru for three years.
The ABC spoke with a witness to the incident earlier this week, who said Omid got distressed during a meeting with UNHCR staff.
“He got very angry and distressed and burnt himself,” she said. “None of them helped. None of them called an ambulance, they just called the police and ran away.
“Doctors didn’t know what to do. They didn’t have supplies to help him.”
The death of the man comes at the end of a tumultuous week which saw the potential collapse of Australia’s offshore processing regime, after Papua New Guinea announced it would close the Manus Island facility under orders from its supreme court.
Australian Medical Association vice president Stephen Parnis, who is an emergency physician, said “questions must be answered” over Omid’s medical treatment.
He said a patient in Australia suffering similar injuries would usually be treated in a specialist burns unit “within hours”, as any delay increases the risk of complications.
“People under the care of the Australian government are entitled to the sorts of standards of care that we would expect in Australia,” Dr Parnis said.
“I think it will be essential that a coroner’s investigation take place.”
Doctors for Refugees convenor Barri Phatarfod said the airlift delay was “unacceptable” and “once again exposes the lie that people offshore have the same medical care as those in the Australian community”.
“We know that the Nauru hospital staff struggled with maintaining an adequate airway and had difficulties accessing an intravenous line,” Dr Phatarfod said. “These are quite difficult to do in a severe burns victim and need a specialised team immediately.”
Before news of the man’s death broke on Friday, Dutton said Nauru was “4500 kilometres from Australia, it is not as if we’re heading out to Bondi or Beenleigh to try and pick up somebody.”
He said there was not a plane “sitting on the runway” waiting to transport ill patients to Australia, and “other medical issues” also affected the timing of the airlift.
A source at Nauru said the man, who lived in the community at the Nibok settlement, poured a 20-litre bottle of petrol over himself and cried: “This is how tired we are, this action will prove how exhausted we are. I cannot take it anymore.”
Human Rights Watch Australia director Elaine Pearson said the “senseless and tragic” death was a direct result of Australia’s “inhumane” policies.
“Refugees who have fled persecution in their homelands don’t deserve a life in limbo in a detention centre or to be effectively imprisoned on a tiny remote island,” she said.“It’s time to save human lives and end this horrible human experiment in offshore detention without further delay.” - PNC sources