The man, who is understood to have been granted refugee status, was allegedly removed without warning or legal representation.
Daniel Webb, the director of legal advocacy at the Human Rights Law Centre, said the man was not a client of his organisation, but did have a lawyer who was not informed of the removal.
"A decent and compassionate government which respects the rule of law doesn't choose to secretively deport people found to be refugees in the middle of the night without any transparency, due process or access to legal advice," said Mr Webb.
Australia's immigration department said it does not comment on individual transfers.
Mr Webb said his organisation represented a group of 300 people - including 100 children - who are in Australia after being transferred from Nauru or Manus Island in Papua New Guinea for medical care. He said the sudden deportation, coupled with prime minister Malcolm Turnbull's talk this week of introducing lifetime visa bans for those detained offshore, was distressing.
"There are kids in our classrooms right now who in the space of the last few days have heard Malcolm Turnbull threatening lifetime bans and now seen someone in a similar situation to them secretly deported. They are understandably afraid and really unsettled," said Mr Webb. "It's fundamentally cruel."
Mr Turnbull said earlier this week that his government was preparing legislation to block migrants and refugees who had been sent to Nauru or Manus Island from ever setting foot in Australia. The lifetime ban would apply to those who attempted to reach Australia by boat, regardless of where they settle and are eventually granted citizenship.
But that proposal has drawn widespread criticism from both advocates and international organisations including Amnesty International, Human Rights Watch and the United Nations, which said it was "profoundly concerned" by the proposal.
The opposition Labor party, which also supports offshore detention, has ridiculed the proposal, but has refused to rule out supporting it through parliament.