Chief health officer Nicola Spurrier is asking event hosts to be aware of at- risk locations and tell guests to stay at home if they visited and haven't returned a negative test.
South Australian authorities issued a quarantine alert for the Intensive English Language Institute at Flinders University between November 13 and 28.
The man in his 30s is believed to have caught the virus as a casual contact at the Intensive English Language Institute at Flinders University.
"And at one point, they were out and about on one particular day and I need to let people know of some places of concern", Prof Spurrier said.
SA Health said shoppers should also isolate immediately.
Two pop-up testing clinics will open this afternoon in Big W Brickworks, Torrensville and Kmart, Kurralta Park.
Prof. Spurrier the decision on whether to charge the man was now in the hands of police. Anyone who visited such locations should monitor symptoms and get tested if they appear.
No new cases were added to the Parafield cluster on Monday which stands at 33, with only 14 of those still considered active.
No new Covid-19 cases were confirmed on Sunday in South Australia.
"What you don't want is somebody who is potentially infectious with this virus, and people have had very minimal symptoms in many cases, coming into a private gathering which is a higher risk because we allow standing up drinking and also dancing", she said yesterday.
Health Minister Stephen Wade said work was also continuing on establishing a dedicated medical facility to care of anyone who tests positive for COVID-19 instead of placing them in hotel quarantine.
On Saturday 3,425 tests were conducted across the state.
"We are not about blaming individuals here, we are about making sure people go and get tested".