South Australian health authorities have identified a "small cluster" of coronavirus cases linked to a Barossa Valley winery, as well as the first suspected instance of community transmission in the state.

Key points: SA Health has linked a number of cases to Lyndoch Hill winery

SA Health has linked a number of cases to Lyndoch Hill winery It is also investigating the case of a woman from regional SA

It is also investigating the case of a woman from regional SA It said she may be the first diagnosis not linked to travel outside SA

The total number of confirmed cases of COVID-19 in South Australia now stands at 170, an increase of 36 in the past 24 hours.

The newest cases range in age from teenagers to people in their 80s, and include a student at the University of South Australia.

SA Health said all of the latest cases were in a stable condition.

Chief public health officer Nicola Spurrier said authorities were also investigating several cases at Lyndoch Hill winery and urged anyone who has been there since March 14 to self-isolate and seek testing.

"We are investigating a small cluster, less than five people at the moment, linked to Lyndoch Hill winery," Dr Spurrier said.

"I'm particularly wanting to put that name out there because we are now trying to do the contact tracing.

"People who attended the winery since the 14th of March and who are now unwell should self-isolate and seek urgent testing."

It comes days after a group of American tourists who travelled to the Barossa Valley tested positive for coronavirus.

On Saturday, SA Health said the American tour group was isolated at luxury vineyard retreat The Louise at Marananga near Seppeltsfield.

The University of South Australia today issued a letter confirming a student had been diagnosed.

It said the student was doing well and students and staff who may have come into direct contact with them were being notified.

"The university today received notification that one enrolled student in our community has returned a positive test for COVID-19," the university's vice-chancellor David Lloyd wrote.

"The student attended our Magill campus last week before being diagnosed.

"All necessary cleaning protocols have been enacted and the campus remains open."

ABC regional office to temporarily shut

SA Health has advised about 200 people who attended a recent function with Senator Rex Patrick, in Cummins on Eyre Peninsula, to self-isolate for a fortnight.

Senator Patrick has tested positive for coronavirus, even though he has reported no symptoms.

An ABC staff member attended the Cummins event on March 17, meaning the ABC will temporarily shut its Port Lincoln office so staff can self-isolate.

None are currently ill or showing symptoms.

"[Senator Patrick] attended a large community meeting in Cummins with around 200 attendees," Dr Spurrier said.

"All attendees at that meeting are classified as close contacts and we are recommending quarantine for 14 days from the date of exposure."

SA Health also said it was investigating the case of a woman in her 50s from regional South Australia, who may be the state's first case of community transmission.

Dr Spurrier said the woman could be the first person not linked to overseas or interstate travel to be diagnosed with COVID-19.

"This is a woman in her 50s, she has had recent contact with people overseas but the information I've been given is that these people did not have symptoms when she was in contact with them which is obviously concerning," she said.

"Because there is up to 14 days' incubation period there may have been more community transmission in South Australia.

"This is exactly why I moved to advise the Minister and the Premier to reduce traffic into South Australia."

Tough new restrictions on cross-border travel came into effect at 4:00pm ACDT.

Anyone whose travel is deemed "non-essential" will be required to self-isolate for 14 days after entering the state.

Dr Spurrier said SA Health was aware of reports David Jones at Marion had closed because a staff member had tested positive.