Australian authorities were racing to track the source of a mystery COVID-19 infection in Sydney on Thursday, the first locally transmitted case in the city in more than a month, warning residents to brace for more cases.

Health officials are baffled by the case of a man in his 50s who tested positive on Wednesday, given he had no known links to high-risk jobs or people.

The New South Wales (NSW) state health department issued an alert naming more than a dozen venues across Sydney visited by the unidentified man in recent days, including restaurants, cafes and shopping centres.

Authorities also asked thousands of residents in the city's innerwest to seek testing for any mild flu symptoms after fragments of the coronavirus that causes COVID-19 were detected in the sewerage network used by several suburbs.

Tests on the infected man showed a higher viral load than typically seen in infected people, potentially increasing the chance that the man has spread the disease, the health department said. Considered to have been infectious since April 30, he was the first case reported in NSW since March 31.

NSW Treasurer Dominic Perrottet entered self-isolation on Thursday after he visited a restaurant at the same time as the infected person, classifying him as a close contact, his office said. Perottet, who attended a sitting of state parliament on Wednesday, has tested negative.

Authorities are investigating whether the mystery case is genetically linked to anyone in the quarantine system or cases in other states, and are also checking which virus variant is involved.

Speedy tracing systems, movement curbs and border restrictions have largely reined in the spread of COVID-19 in Australia, which has recorded 29,865 cases and 910 deaths since the pandemic began.

The federal government is currently under pressure to overturn a temporary travel ban on travellers, including its own citizens, from COVID-ravaged India. Australia has blocked all direct flights from the country until May 15.

A report in the Sydney Morning Herald newspaper on Thursday, citing unidentified sources, said at least two repatriation flights will be dispatched to India every week from the middle of this month to bring home around 9,000 Australians.

Prime Minister Scott Morrison, however, said the situation would be reviewed after May 15.

"We are not going to commit to that at this point," Morrison told radio station 3AW on Thursday.