South Australia has reintroduced a number of significant restrictions in response to a coronavirus cluster in Adelaide's northern suburbs.

Premier Steven Marshall said all inbound international flights to Adelaide have been cancelled for the remainder of this week and the Australian Defence Force will be mobilised in South Australia.

Chief Public Health Officer, Professor Nicola Spurrier, said the despite significant rates of testing today, no new cases had been identified beyond the 17 confirmed this morning.

Premier Steven Marshall thanked the people of South Australia for flocking to get tested.

"We are facing our biggest test to-date," Mr Marshall said.

"We must act swiftly and decisively to stay ahead of the game."

There are currently 34 active cases in South Australia including repatriated citizens in hotel quarantine.

Mr Marshall said from midnight tonight, a number of restrictions would be reintroduced for the whole of South Australia, including:

The Premier also urged people to work from home if they could, asked for all unnecessary travel plans to be cancelled, urged masks to be worn when social distancing was not possible and encouraged vulnerable people to stay home and avoid visitors.

Chief Public Health, Professor Nicola Spurrier, said putting restriction in place was the best way to get ahead of the cluster.

"The first thing we need to do … is the testing, contact tracing and getting people into quarantine very, very quickly.

"The other way of getting ahead of this and to stop that second wave, and to suppress it, is to put some restrictions in place to reduce the number of close contacts between people."

She said the cluster "is clearly from a medi-hotel" but genomic testing was ongoing.

"We have tested the two people who are security guards from a medi-hotel and the one person that works in the medi-hotel from back of house and we are waiting to have that genomic analysis," she said.

"Then we will be able to link exactly to which person they were able to get it from."