A case of COVID-19 has been diagnosed in a man who lives in Sydney's eastern suburbs, with authorities yet to determine how he caught the virus.

A man from Sydney's eastern suburbs has been diagnosed with COVID-19 but there's no indication where he picked up the virus.

NSW Premier Gladys Berejiklian says the man in his 50s has not recently travelled overseas, does not work in a hotel quarantine, border or a health role, and has no idea where he caught the coronavirus.

He also had not recently travelled interstate.

The man's positive result was recorded on Wednesday morning and NSW Health believe he has been infectious since last Friday.

NSW Health contract tracers are urgently working to identify any contacts and genome sequencing is underway, with results expected in the next 24 hours.

The man has a number of close contacts who are being tested and are isolating, NSW Chief Health Officer Kerry Chant says.

He also visited a number of venues while potentially infectious, she said, but had been meticulous about checking in using QR codes.

"This person did everything right, but it goes to show that we can't take a single thing for granted," Ms Berejiklian told reporters on Wednesday.

"It goes to show we have to maintain our social distancing, have to make sure we have good hand hygiene, we need to get tested with the mildest of symptoms, and very importantly and significantly, we need to use QR codes."

A list of venues of concern has been compiled which includes a number of barbecue stores in Silverwater, Annandale and Casula, a meat store in Bondi Junction and a petrol station in Mascot.

The man also attended a screening of The Courier at Event Cinemas Bondi Junction on Friday before attending Figo Restaurant at Rushcutters Bay.

Later on Wednesday, three new venues were listed - District Brasserie restaurant in the Sydney CBD, Barbetta restaurant in Paddington and HineSight Optometrist inside the Sofitel Sydney Wentworth.

People who have attended those venues at various times between April 30 and May 2 should get tested and self-isolate until they receive further advice.

The man has not yet received a COVID-19 vaccine, Dr Chant said.

Ms Berejiklian said it was too early to say if coronavirus-related restrictions need to be tightened in NSW but anticipated more locally-acquired cases.

"We have to assume there's other cases and our response will be proportionate as it always has been in NSW," she said.

"Everybody in the state needs to be on high alert.

"Anybody anywhere with the mildest of symptoms needs to come forward and get tested if you have been in those venues at those times and have mildest of symptoms."

Ms Berejiklian also encouraged all eligible people to get vaccinated.

People 50 and older have from Monday been able to get immunised at some Commonwealth-run respiratory clinics across Sydney.

Federal Health Minister Greg Hunt said on Wednesday: "We know the strength of the NSW system, the absolute global gold standard."