The New South Wales health authority issued an alert late on Tuesday about two flights between Wellington and Sydney linked to the case.
It said passengers who were on one flight into Wellington, and one flight back to Sydney last weekend, are considered close contacts of a COVID-19 case.
The flights were Qantas QF163, which left Sydney at 7.05pm on Friday 18 June and landed in Wellington at 12.12am on Saturday; and Air New Zealand NZ247, which left Wellington at 10.13am on Monday 21 June, arriving in Sydney at 11.33am.
The Australian state's health authority is urging anyone who was on those flights to get a COVID-19 test, and to self-isolate for 14 days, regardless of the result.
New Zealand's Ministry of Health said stage four close contacts had been identified and are isolating. The ministry said it would advise sites of interest that were visited in New Zealand as further contact tracing is undertaken.
Based on the time of the onset of symptoms and the CT score it is most likely the person had contracted the virus in Sydney before to their visit to New Zealand, the ministry said.
The Ministry of Health's contact-tracing team has been in touch with the airlines about contacting passengers on the two flights to provide advice.
This is the first time an Australian traveller has brought COVID-19 to NZ, and since gone home, the ministry said.
Genome sequencing was underway in Australia to see if the case is linked to the current outbreak in Sydney.
Quarantine-free travel from New South Wales to New Zealand had already been temporarily suspended due to the rising case numbers in Sydney, and will last at least 72 hours.
The Australian state yesterday recorded 10 new cases of COVID-19, and health authorities announced new exposure sites there.
The latest surge in cases in the Sydney Bondi cluster led NSW Premier Gladys Berejiklian to extend the state's mask mandate for all indoor public venues to midnight Wednesday 30 June.
Local government areas of Wollongong and Shellharbour, which had compulsory masks for public transport, would be subjected to the same mask rules as Sydney.
The Westfield Bondi Junction shopping centre continued to be the main area of concern to health authorities on Tuesday.