From midnight on Tuesday, family gatherings will be limited to 10 people, down from 50, and pubs and restaurant patrons must be seated.

SA is also looking at all density requirements, which currently require only two square metres for each person, and is likely to cut the number of people at AFL games from about 20,000 to around 10,000.

Premier Steven Marshall said the changes were about being proactive in the face of the growing threat.

"Australia is on high alert," he said.

"We're extraordinarily concerned about the Victorian outbreak and the potential for seeding in other jurisdictions.

"We will continue to act swiftly, to trust the experts and keep ahead of the game."

The changes to restrictions came as two new COVID-19 cases were reported in Adelaide on Monday.

Both involved men in their 50s, one a close contact to an existing case and the other a person who arrived in Adelaide at the weekend on a repatriation flight from India.

The two cases took the number of active infections in SA to eight.

Chief Public Health Officer Nicola Spurrier said the latest cases were "very concerning".

"We've now seen transmission within our state to close contacts of cases," she said.

"This absolutely reflects the situation in Victoria ... of how transmissible this virus is."

The new cases also came as five people were to appear in court in SA charged with breaching the state's border rules.

In one case a 25-year-old man admitted he crossed from NSW to pick up his cousin's dog after previously being turned around at the Victorian border.

He was arrested in Adelaide on Saturday and given a suspended jail sentence.

His passenger, a 20-year-old woman, was put on a good-behaviour bond.

Mr Marshall said SA would not be changing its border rules anytime soon.

Under those arrangements, anyone crossing from Victoria must be an essential traveller while anyone coming from NSW or the ACT must quarantine for 14 days.

Australian Associated Press