SA still a chance to stop virus: premier

"We've got one shot to stop this outbreak dead in its tracks," SA Premier Steven Marshall says.

South Australia will bolster testing resources amid growing COVID-19 cases and exposure sites but an optimistic premier says the state still has a chance to "nip this in the bud".

One new case was reported on Wednesday, taking the current cluster to six on the first full day of a week-long statewide lockdown.

A woman in her 20s was working at The Greek restaurant in Adelaide last weekend where a birthday party was held involving previously infected guests.

Authorities fear the party could become a superspreader event.

The woman also works at the Westminster School, where she attended teacher training on Monday, although students had not returned from school holidays.

Premier Steven Marshall said as the number of exposure sites grew to more than 50, the state would do everything it could to increase testing resources amid reports of long lines forcing some to wait for more than 10 hours.

Mr Marshall said officials were "pulling every single lever possible" to increase testing capacity with Defence personnel, both local and interstate, to help and interstate nurses and doctors to lend further assistance.

Changes would also include the opening of a dedicated facility for those people directed to get tested and enter home quarantine and the publishing of estimated wait times for all of SA's more than 80 testing sites.

"We don't want people angry and frustrated with delays. We are ramping up capacity across testing sites," the premier said.

"We've got one shot to stop this outbreak dead in its tracks.

"We've got a chance to nip this in the bud. We don't want to have an extended lockdown in South Australia."

SA's list of exposure sites includes major shopping centres and schools.

Chief Public Health Officer Nicola Spurrier said two of those were of most concern, The Greek restaurant and the Tenafeate Creek winery at Yattalunga, north of Adelaide.

She said almost 6000 people linked to all exposure sites were now in home quarantine.

SA's virus cluster is linked to an 81-year-old man who recently arrived in Australia from Argentina and quarantined in Sydney before travelling to Adelaide, where he tested positive.

Genomic testing has confirmed the man became infected while in Sydney, not while in Argentina.

During the week-long lockdown, which started on Tuesday evening, South Australians will only be allowed out for five reasons - to provide essential care, to seek medical assistance, to buy essential food and other goods, for essential work, or to exercise for up to two-and-a-half hours.

They must also wear masks when outside their homes.

Schools have closed along with most retail outlets and all construction work has ceased.

Police Commissioner Grant Stevens said the SA community was doing a good job in complying with lockdown rules.

"Every indicator we've seen so far is that people are doing the right thing," he said.

"Streets are empty, the city is empty.

"I'm as hopeful as anyone else that we can keep this lockdown to seven days, but there's a lot of work to be done."

Other jurisdictions have also acted swiftly to put restrictions on people coming from SA, with Tasmania and Queensland closing their borders and Western Australia and the Northern Territory requiring people to quarantine.

Australian Associated Press