A woman in her 50s and man in his 60s were later tested and on Sunday also found to be infected.
“One of those people works in our medi-hotels,” said Spurrier.
“This is where we are considering the source to be.”
Spurrier said the infected trio has a very large family and four relatives were showing symptoms with test results expected later in the day.
The older woman lives independently not in an aged care facility and is now in isolation at the Royal Adelaide Hospital.
She is the mother of one of the younger pair, who are in a relationship.
Contact tracing is also underway for about 90 staff and patients at the Lyell McEwin Hospital who may have come into contact with the 80-year-old woman.
Spurrier said the woman also visited Parafield Plaza Supermarket in Adelaide’s north while infectious.
She urged any person who develops symptoms to immediately report for testing.
“I am expecting that we will have more cases. This is a wake-up call,” said Spurrier.
All staff working at SA’s quarantine hotels will now be required to undertake virus testing every seven days.
“It’s obvious that this is the highest risk in Australia right now is this risk of importation (of the virus) in our quarantine hotels,” Spurrier said.
The new rule includes police, nurses, concierge, cleaners and security guards.
A 30-year-old man in hotel quarantine who recently returned from overseas was also diagnosed with the virus on Sunday.
There are now 19 active COVID-19 cases in SA.
By Aaron Bunch