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South Australia is moving into a full seven-day lockdown after a cluster of local COVID-19 cases grew to five.

The fifth case, a man in his 60s, is someone who dined at a restaurant in Adelaide where previously infected people were also present on Saturday night.

Those people had all attended a birthday party in a private function room which authorities said had the potential to act as a super-spreader event.

The lockdown rules come into effect from 6pm on Tuesday with South Australians only allowed out for five reasons.

Premier Steven Marshall said it had also been confirmed the current cases involved the Delta variant of the disease.

"We hate putting these restrictions in place but we have one chance to get this right," the premier said.

"We are moving as quickly as we can to slow and stop the spread of this cluster.

"We know these restrictions will take a heavy toll. But we've always had a situation where we go hard and we go early in South Australia.

"We've got to stop movement around this state and we've got to stop it immediately."

South Australians will only be allowed out of their homes for essential care, essential work, the purchase of foods and essential goods, for medical reasons and for limited exercise.

As the number of cases and exposure sites continued to grow, authorities said more testing sites would open with the first of those a drive-through facility at Ridgehaven, in Adelaide's northeast.

SA Pathology boss Tom Dodd said as many resources as possible were being dedicated to testing, including a new drive-through site at Ridgehaven in SA's northern suburbs.

He also thanked people who queued for hours for testing, including many who were forced to sleep in their cars overnight.

"It's inevitable whenever there is a case identified there will be a huge increase in testing," he said.

"We don't want people to queue for an inordinate amount of time, so we thank people for their patience."

The outbreak has plunged thousands of people into quarantine with the list of more than a dozen exposure sites including at least four major shopping centres in Adelaide's north and northeastern suburbs.

Chief Public Health Officer Nicola Spurrier said the number of sites would increase on Tuesday as she urged everyone, especially those in isolation, to stay home.

"The virus doesn't have legs, it moves around when people move around," she said.

"So if people stay put we will able to get on top of it."

Professor Spurrier said contact tracing was underway in regard to the fifth positive case which was confirmed early on Tuesday morning.

She said the situation was currently more dangerous than when SA had an outbreak of cases known as the Parafield cluster in November last year.

"It's a very dynamic situation," she said.

The new SA cluster began with an 81-year-old man who entered the country from Argentina, his daughter and another two men.

He had returned to Australia via NSW, where he spent 14 days in quarantine.

He arrived back in SA on July 8 and presented to a suburban hospital over the weekend after developing symptoms.

© AAP 2021

Photo: South Australian Premier Steven Marshall (AAP Image/Kelly Barnes).

South Australia has imposed widespread coronavirus restrictions, including closing all non-essential retail outlets, following the discovery of a second COVID-19 case.

The daughter of an 81-year-old man has now tested positive along with her father after the pair arrived from Argentina some time ago.

Premier Steven Marshall says five other close contacts of the pair have tested negative so far but authorities are very concerned about the current situation.

"We only have one chance to get this right. Our focus from day one has been to go hard and to go early to minimise the level of disruption," he said.

"We've got to respond quickly."

New SA restrictions include a density change to one person to every four square metres in all venues, while all team and contact sport is to be cancelled.

All dining will need to be seated with a ban imposed on dancing and singing.

Masks will be required in all public outlets, including shopping centres.

Fitness centres will be closed along with other non-essential retail outlets. Supermarkets and pharmacies and other essential businesses will continue to trade.

Schools will stay open.

The new rules will apply from midnight on Monday and will be reviewed on Friday.

Police Commissioner Grant Stevens said while SA was not moving to a full lockdown, the restrictions were significant.

"We know there are people who will struggle as a result of these changes. But the consequences of not taking action could be even more severe," he said.

"The intent here is to dramatically suppress all discretionary activity in the community."

Authorities said earlier that the elderly man had returned to Australia through NSW, where he spent 14 days in quarantine.

He spent a further 10 days in hospital in NSW after suffering a fall before returning to SA on July 8, and presented to a suburban hospital over the weekend after developing symptoms.

The man had received one vaccine dose while in Argentina, but it was not known what type.

The man has been admitted to hospital, while his daughter has been taken to the Tom's Court Hotel which is used to quarantine all positive COVID-19 cases.

"We don't draw any conclusions as to where this infection came from. We simply don't know and it is very early days," Mr Marshall said.

"Our primary concern at the moment is putting everyone who may have come into contact with this person into quarantine as soon as possible."

Mr Marshall said the emergency department at Modbury Hospital remained closed while a risk assessment is performed, and would be progressively opened when it was safe to do so.

Some staff have been placed in quarantine.

The premier said the Elizabeth Vale Primary School would also reopen on Tuesday after being closed on Monday.

The school was closed as a precaution while checks were made to ensure the elderly man's grandson, who is a teacher, didn't attend over the two-week holiday period.

SA Health named five potential exposure sites, including an OPSM store at Golden Grove, a food warehouse at Hindmarsh, the Commonwealth Bank at Modbury and an Aldi Supermarket at St Agnes.

There is also some concern for an outdoor reserve at Glenelg.

Chief Public Health Officer Nicola Spurrier said officials were assuming the man had the Delta variant of the disease, though that was yet to be confirmed.

She said it was known the Delta strain could "spread like wildfire".

© AAP 2021

Photo: South Australian Premier Steven Marshall in November 2020 (AAP Image/Kelly Barnes)