The new case is a man in his 60s who last weekend visited the Tenafeate Creek winery near One Tree Hill, north of Adelaide, which is now linked to nine infections.

The SA outbreak now stands at 16 cases.

South Australian Premier Steven Marshall said with the new case already in quarantine, the state remains on course to emerge from its seven-day lockdown on time.

"There's still some way to go but all of the signs are the people of South Australia are taking this extraordinarily seriously," he said.

"So a massive, massive thank you. I feel proud to be South Australian."

Mr Marshall said it also showed the importance of taking early action to prevent the spread of the virus.

"If we had waited another 12 or 24 hours we know that this particular strain would have got away from us," he said.

"This disease thrives on indecision. We moved very quickly in South Australia to put restrictions in place and I'm very hopeful we'll be able to come out on day seven."

As part of its action, SA will cancel international flights due into Adelaide on Monday and Tuesday.

It also continues to ramp up testing capacity with 23,410 swabs processed on Friday.

One new testing centre opened on Saturday with another, to be run by the defence force, close to operational.

An online booking service is being implemented.

However, bad weather on Saturday morning forced the temporary closure of the Victoria Park 24-hour site, Adelaide's largest.

Nevertheless, Mr Marshall said wait times were now no more than an hour at all testing sites, down from more than 12 hours at one stage.

As well as the cases linked to the winery, a number of other infections in the SA cluster have been linked to The Greek restaurant in Adelaide.

The restaurant and the winery are considered superspreader events.

SA's list of exposure sites has grown to about 80, with about 18,000 people thought to have visited at least one during the relevant times.

About 4000 of those are in home quarantine after being considered at higher risk.

SA's virus cluster began with an 81-year-old man who recently arrived in Australia from Argentina and was 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.

Signs of the man's infection may also have been present in wastewater samples checked in Adelaide's northeast which returned a positive result last weekend.

Chief Public Health Officer Nicola Spurrier said it was initially thought the wastewater result involved someone who had previously had an infection while in hotel quarantine and was still shedding the virus after release.

"In retrospect ... it's likely that the family with this older gentleman was responsible for that positive," she said.

Australian Associated Press