A CA statement later said: "Our bio-security and operational teams are closely monitoring the situation".
A cluster of cases in Adelaide prompted other states like Western Australia, Tasmania and the Northern Territory to close their borders with South Australia and impose a 14-day hotel quarantine on all visitors from Adelaide from Monday noon.
Police Commissioner Grant Stevens said of the people being moved to a new location, some considered low risk would be allowed to do so by themselves while others would be escorted by health officials.
"This is a very risky situation".
Fearful of case numbers spiralling, authorities snapped back a swathe of coronavirus restrictions and suspended global flights into Adelaide.
All but two of the 17 were members of the same large family, including one who was working in a hotel used to quarantine travellers returning from overseas.
"It is a very risky situation that we're in here in South Australia at the moment, and it's really going to require the cooperation of every single citizen for us to get on top of this, " state premier Steven Marshall told local radio 5AA on Monday.
He urged any South Australian with even mild symptoms to get tested.
Similarly, the Adelaide Strikers have been forced to flee their home city, setting up a pre-season base at Coffs Harbour on the north coast of New South Wales, prior to the commencement of the Big Bash League.
"What this does is reinforce for us how contagious the disease is and how unexpectedly cases and outbreaks can arise".
"We just kept getting positives coming off the machine", South Australia Chief Public Health Officer Nicola Spurrier told the Australian Broadcasting Corp.
Western Australia, which borders South Australia, said it was introducing mandatory virus testing and a 14-day quarantine for interstate arrivals, tightening its border control soon after letting in people from elsewhere in the country.
Australia has recorded about 27,800 novel coronavirus infections and 906 deaths.
The country's internal borders had been gradually reopening and were due to be nearly fully reopened by Christmas.