Hundreds of people died when conflict erupted in the capital Juba two weeks ago.
Community members in Australia say former Queensland resident Jacob Diu was caught in the crossfire.
A former social worker from Brisbane, Mr Diu, also known as Jacob Jok Gai, had returned to work in his homeland six years ago.
He was killed, along with his adult son who was visiting him from his home in India.
His son was not an Australian citizen.
The exact circumstances of their deaths cannot be independently verified.
But the president of the South Sudanese Communities in Queensland, Daniel Lee, says Jacob Diu was shot.
"What happened to Jacob is tragic. He was in the wrong place at the wrong time. He shouldn't have been there. But he didn't know. So he got caught up in the crossfire, right in front of the presidential palace in Juba."
The incident came amid violent clashes between forces loyal to President Salva Kiir and those loyal to Vice-President Riek Machar earlier this month.
Hundreds of civilians and soldiers were killed and injured before a shaky ceasefire was declared four days later.
Mr Lee says Mr Diu's death in the unrest has come as a shock.
"The family's devastated. I mean, nobody, not even us in the community, has envisaged such a tragic event to unfold within the community, especially at this time, because Jacob has been a complete part and parcel of this community in Queensland. He has been a founder of much goodwill in Queensland."
Australia has no diplomatic presence in South Sudan.
Nearly a fortnight after the death, the Department of Foreign Affairs told SBS, it is still seeking official confirmation that an Australian-South Sudanese dual national has died.
Berhan Ahmed, from the Melbourne-based African Thinktank, says that is not good enough.
"Well, it's quite appalling, because, in this day and age, Australia always cries out for every Australian, but when it comes to non-white, always we become non-existent. There were cases in Iraq, there were cases in many other countries, that Australia has ignored. And this is not fair. What leadership is telling the general public (is) that you are more important than the others, and this is not a way forward for the nation to build cohesion and harmony."
Daniel Lee says no-one from the Australian government has contacted Jacob Diu's family in Brisbane.
He says the community is unaware of what help the Australian government could, and should, provide.
"We are not blaming the government or blaming anybody. It's only that we haven't known that there will be something that the government should do for us and sort of asking what is happening. A lot of us are dual citizens of this country. This is where we are. We go back either way to visit family or to do some work there. We are not sure what is supposed to be the role of the government in such a tragic event."
