Chief Minister Michael Gunner said the recent outbreak in SA was alarming and warranted swift action.

He said arrivals from South Australia would either be directed to quarantine or offered the option of returning home, that even applies to people already travelling today.

Mr Gunner said despite the SA outbreak, numbering 17 today after only being reported on the weekend, Melbourne's restrictions were on target to being reduced.

He said Melbourne would no longer be a hotspot from November 30.

"This is much sooner than any of us expected."

Mr Gunner said health officials would continue to monitor control progress in Melbourne but many consecutive days of zero cases had been better than expected.

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Tasmania, Victoria and Western Australia have immediately joined the Northern Territory in declaring South Australia a hotspot.

South Australia recorded its first locally acquired case in almost three months on Sunday, with four cases reported.

The cluster began when a woman in her 80s tested positive for the virus on Saturday.

Two family members were also part of the original cluster, which included a man in his 60s who works in hotel quarantine for returning travellers. SA Health has said that is likely the source of the outbreak.

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