South Australia is staring down a new coronavirus cluster, with four people outside of hotel quarantine diagnosed with COVID-19.

SA Health said on Sunday an 80-year-old woman had tested positive after being treated at the Lyell McEwin Hospital in Adelaide's northern suburbs.

Two of her close contacts — a woman in her 50s and a man in his 60s — have also tested positive for the disease.

Chief Public Health Officer Nicola Spurrier said one of them worked in Adelaide's CBD at one of the state's medi-hotels — accommodation used by incoming travellers and local residents who could not safely quarantine at home.

One of the infected people is the elderly woman's child.

Four other family members were showing symptoms, Dr Spurrier said.

Later on Sunday, authorities said a fourth person linked to the growing cluster in Adelaide had been infected.

An email from SA Correctional Services chief executive David Brown said an employee at Yatala Labour Prison in Adelaide's northern suburbs had tested positive.

The email said the person was identified as a close family contact of one of the positive cases reported on Sunday afternoon.

It is not yet known when the employee was last at the prison, or whether they had contact with the prisoners.

The Department of Corrections said it was in the process of activating a health rapid response team to assist with contact-tracing efforts at the prison.

All employees had been asked to remain at their posts to assist with this, it said.

The email said a female prisoner from a different Corrections facility had also been affected because she was at the Lyell McEwin Hospital emergency department during the time a positive case was there.

The email said the prisoner was still at the hospital.

Dozens told to quarantine, hotel suspected to be source

South Australia's last positive case without a known source of transmission was reported on April 16 — seven months ago.

Dr Spurrier said in this case, the medi-hotel where one of the infected people worked was likely to be the source of the positive cases, but she said it was "very, very early information" and genomic testing would be undertaken to determine the source.

"Obviously this is where we're considering the source to be," Dr Spurrier said.

She warned more people were likely to be infected.

"Which is why I am absolutely warning South Australians: This is a wake-up call — if you have respiratory symptoms, you've got to get tested," she said.

About 90 people who were in the hospital's emergency department at the same time as the 80-year-old infected woman — between 5:30pm on Friday and 4:00am on Saturday — have been ordered to quarantine.

Dr Spurrier said the woman also visited the Parafield Plaza Asian supermarket between 10:30am and 11:30am on Thursday while she was infectious.

Anyone who was there at the same time should monitor themselves for symptoms.

On Sunday evening, an Adelaide primary school said it would close on Monday to undergo a deep clean due to a student being identified as a close contact of a positive coronavirus case.

The Department of Education said Mawson Lakes Primary School and Preschool, in Adelaide's northern suburbs, would close for at least 24 hours out of "an abundance of caution".

The department said people who needed to self-isolate would be contacted directly.

WA changes entry rules for SA travellers

Following the news of the new cases, WA's Police Commissioner, Premier and Chief Health Officer decided at an emergency meeting to test anyone arriving at Perth Airport from South Australia and direct them to self-quarantine for 14 days.

Those affected included passengers from a Qantas flight to Adelaide from Perth that had just arrived in the city.

People who had entered the state by plane were given the option of flying back to Adelaide on Monday after being told of the changes on arrival.

Passengers due to arrive on a flight later on Sunday were told about the new requirements and given the option to disembark.

Anyone arriving in Western Australia by road from South Australia will be told to follow the same self-quarantine and testing rules.

Anyone who arrived in the state from South Australia on Saturday or Sunday will be contacted by WA officials and will be required to be tested for COVID-19 and self-quarantine until results are returned.

More than 500 cases in SA since pandemic began

From Sunday, all staff at South Australian quarantine hotels will get tested for coronavirus every week, Dr Spurrier said.

A total of 526 coronavirus cases have been reported in South Australia since the beginning of the pandemic, including 19 active cases.

Four people have died.

The Victoria Park drive-through coronavirus testing clinic has reopened after previously being closed because of lightning.