Canberra has sent asylum-seekers who try to enter the country by boat to camps on PNG's Manus Island or Nauru in the Pacific for processing, with those found to be refugees barred from resettling in Australia.
The harsh policy is meant to deter people embarking on treacherous sea journeys, but the United Nations and other rights groups have criticised the camps' conditions and long detention periods.
Australia's home affairs department confirmed the death but did not provide further details.
The Refugee Action Coalition's Ian Rintoul told AFP the man, a 32-year-old called Salim, was believed to have jumped from a moving bus near a refugee transition centre and was struck by its wheels, dying at the scene.
Most asylum-seekers on Manus believed the man's death was a suicide, according to a statement from the coalition.
He was the seventh asylum-seeker to die on Manus since Canberra's offshore detention regime began in July 2013, in addition to three others who died on Nauru over the same period, Rintoul said.
"The Rohingyan refugee had suffered for a long time with a medical problem" and had previously been sent to Australia for treatment, he added in a statement.
Behrouz Boochani, an Iranian refugee on Manus, tweeted Tuesday that Salim had epilepsy and was "suffering for a long time".
Previous deaths on Manus include an Iranian refugee found hanging from a tree near a school in August last year, and a Sri Lankan Tamil asylum-seeker who reportedly committed suicide at a hospital two months later.
The Australian camp on Manus was shut late last year after a PNG court ruled it was unconstitutional, with the 600 detainees sent to three transition centres.
Canberra has sought to offload those recognised as refugees to third countries such as the US, and more than a hundred have been resettled there, according to reports.
But hundreds of others remain on Manus, saying they feared for their safety amid hostility from the local population, and that their basic needs such as healthcare were not being met.
The UN refugee agency said Salim's death showed the need for "proper care and immediate solutions".
"With the passage of too many years and the withdrawal or reduction of essential services, the already critical situation for refugees most in need continues to deteriorate," UNHCR's regional representative Nai Jit Lam said.//AFP