South Australian authorities say they are facing a "dangerous situation" after reporting 18 coronavirus cases in the state's first outbreak since April.

Up to 13 infections were linked to a hotel quarantine worker in Adelaide who spread the virus to a family in the local community, officials said.

The state has ramped up testing and brought in new restrictions.

Australia had seen cases drop to near zero after beating a second wave that was largely confined to Victoria.

Victoria's capital, Melbourne, spent almost four months in a stringent lockdown before re-opening last month.

• How Melbourne's long lockdown crushed a second wave

Its outbreak - which caused about 800 deaths - also originated from a hotel quarantine breach.

"It's obvious that the highest risk in Australia right now is this risk of [virus] importation in our quarantine hotels," South Australia's chief health officer Nicola Spurrier said on Monday.

State Premier Steven Marshall added: "We are facing our biggest test to date. We are working around the clock to stay ahead of this cluster - no effort will be spared."