The Iranian man, named by refugee advocates as 24-year-old Hamid Kehazaei, was transferred to Australia from Papua New Guinea last month after reportedly developing septicaemia.
But doctors were unable to save him.
"The man's family late this afternoon provided consent for the withdrawal of his life support," Immigration Minister Scott Morrison said in a statement late yesterday.
"An imam was present at the time of death and the government of Iran will be informed."
Under Canberra's hardline immigration policy, asylum- seekers arriving on unauthorised boats are denied resettlement in Australia and sent to PNG or the Pacific island of Nauru.
In offering his condolences, Morrison said the immigration department's chief medical officer was conducting an in-depth clinical review of the man's care.
The minister said he would await the results of this review before making further comments, but noted that "the criticisms that have been made to date are not based on any primary knowledge of the event or the circumstances in this case".
"They said to me without any reservation that what they want is for justice for Hamid," she told the Australian Broadcasting Corporation.
"They want answers about the events leading to Hamid's transfer to Australia and how their son, why their son died as a result of such a non-threatening condition whilst in Australia's care. Because this just does not happen in a civilised society."
Hudson said an open and independent was inquiry needed to assess whether Kehazaei received antibiotics to treat the infection soon enough.
Papua New Guinea police have charged two men over Barati's murder.
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