Health and government authorities approved a family with COVID-19 to fly in from overseas to Australia last week on a privately-funded medevac flight, despite ongoing calls to limit the number of international arrivals.

Health authorities knew the family was positive for coronavirus before approving the flight, which SA Health confirmed was the first of its kind to land in South Australia since the pandemic began.

COVID-positive patients have previously been denied the right to board repatriation flights back to Australia.

In a statement, South Australian Deputy Chief Public Health Officer Emily Kirkpatrick confirmed the family arrived in the state last week.

"A family — a male and female adult and a child, from South-East Asia — were repatriated into South Australia last week by a private medical evacuation company," Dr Kirkpatrick said.

SA Health said the child had been cleared of COVID–19, while the adults were in Tom's Court — a medi-hotel used exclusively for COVID-positive patients.

The family was made up of "unwell Australian citizens" and the flight was in addition to the state's international arrivals cap. 

The medical evacuation flight was paid for by the family.

SA Health and federal officials sanctioned the flight and arranged ground transport and the use of the medi-hotel system.

Dr Kirkpatrick said the flight crew was managed in the same way as flight crews aboard other repatriation flights.

"The crew had a one-night layover in a medi-hotel, tested negative and returned overseas," she said.

Premier Steven Marshall said he had no part in the flight approval process.

"I don't have any information that they are politically linked," Mr Marshall said.

SA Chief Public Health Officer Professor Nicola Spurrier said normal procedure for medical retrievals in the region was followed.

Professor Spurrier said the family were Australian citizens who lived in Adelaide, but were working overseas.

"It's done as a hospital-to-hospital transfer ... this happens on a fairly regular basis in the eastern states," Professor Spurrier said.

She said the transfer was "not about wealth" and said it was a different situation to those people who were barred from coming back to Australia after testing negative in India.

"You cannot have a medevac flight going to India — the planes are too small it's simply not possible," she said.

"This is a pre-existing way of retrieving people who are working close to Australia. Of course, any of those exemptions for those people to come into Australia are given by the Commonwealth."

The Department of Foreign Affairs and Trade has declined to comment.

Australian Border Force has been contacted for comment.

The details were revealed at a press conference that confirmed a family had tested positive to COVID-19 in SA after a man in his 30s contracted the illness while working at an NT mine site.