Authorities believe the man, who has not been vaccinated, has been infectious since Friday.
He had not been overseas or worked in Sydney's hotel quarantine system so authorities were keeping an open mind while working to find the source of the infection, NSW chief health officer Dr Kerry Chant said.
She said authorities hoped genome sequencing would identify the source of the infection, which could be from interstate.
Chant said the man's cycle threshold (VT) values were low, which meant he had a higher viral load and was potentially more infectious.
"So they do give us cause for concern," she said.
The man did "everything right" according to the premier and his direct contacts were in isolation and undertaking Covid-19 tests.
Berejiklian said she was expecting more positive cases.
"If there is one case and there's no direct connection, we have to assume there's other cases. Our response will be proportionate as it always has been in NSW."
Anyone who has attended the following venues must get tested and isolate immediately:
- Event Cinemas at Bondi Junction Westfield 30/4/21 6pm-8pm local time
- Figo Restaurant, Rushcutters Bay 30/4/21 8.45pm-11pm
- Joe's Barbeques & Heating, Silverwater 1/5/21 1pm -1.45pm
- Tucker Barbecues, Silverwater 1/5/21 1pm-1.45pm
- Barbeques Galore, Annandale 1/5/21 2pm-3pm
- Barbeques Galore, Casula 1/5/21 4pm-5pm
- BP 1077 Botany Road, Mascot 1/5/21 4.30pm-5pm
- The Meat Store, Bondi Junction 2/5/21 3pm-4pm
Chant said she did not believe the man was infectious at his workplace and her main focus was whether he had passed the virus onto his close contacts, of which she said there are about two dozen.
"Understanding the source will be really important to understand how many cycles we have seen in the community that we haven't recognised yet," Chant said.
She reminded the public that even those who have had one or two doses of the Covid-19 vaccine must still get tested and isolate, with pop-up testing clinics set to be announced later today.
Health Minister Brad Hazzard said those in the eastern suburbs needed to stay across all health messages in the coming days with more venues expected to be placed on alert.
"We've said time and time again, the world is a very dangerous place [right now] and in this case, the eastern suburbs may or may not be."
Berejiklian said everyone across the state must be following health precautions with renewed vigilance.
"When there is a case and we don't know the source, all of us have to be on guard, no matter where you live. All options are on the table ... it means, unfortunately, we can't rule anything out," she said.