He flew into Australia on the same flight from Doha as a woman aged in her 30s who was confirmed to have the variant on Tuesday, but NSW Health says there's currently no evidence transmission occurred on the flight itself.
Another COVID-19 case who had been isolating at home in Broken Hill after disembarking that flight has been confirmed to have the Delta variant.
Tuesday's confirmation of a fifth case sparked a number of alerts after she visited several stores and shopping centres.
However, the latest case has sparked just one alert after a five-minute visit to a Liverpool chemist on Monday morning.
NSW Premier Dominic Perrottet is calling for calm, saying Omicron "was always going to get here".
"We're getting asked questions here about six cases," he said on Wednesday.
"Let's shift the thinking ... It's not about the case numbers. It's about the hospitalisations and the ICU presentations."
NSW Health Minister Brad Hazzard says the government is not considering another lockdown.
"I feel like it's time for a change in approach," he said.
"We don't know how many more variants of this virus are going to come.
"The challenge for us as a government and the other governments ... is to strike a different balance to the ones we had in the past."
When national cabinet met on Tuesday the federal, Victorian and NSW governments agreed they were "not keen to see a return to lockdowns".
Restrictions will instead be "tailored" if there are health concerns, Mr Perrottet said, with the next stage of the state's roadmap out of lockdown due on 15 December.
The man who was confirmed positive for Omicron on Wednesday and the woman who was confirmed the day before are in isolation, having arrived before travellers coming from eight southern African countries were directed to 14-day quarantine.
The other four people confirmed to have the Omicron variant are in special health accommodation after arriving on the weekend.
Brad Hazzard announces sixth case of Omicron variant discovered in NSW
NSW now requires all other international arrivals be tested and isolate for 72 hours at a nominated address or accommodation.
On Wednesday, the penalty for non-compliance with isolation, testing and quarantine requirements increased from $1000 for individuals to $5000, and doubled from $5000 to $10,000 for corporations.
The state recorded 251 new cases of COVID-19 and no deaths in the 24 hours to 8pm on Tuesday.
Some 94.6 per cent of people 16 and older have had one vaccine dose, while 92.6 per cent are fully jabbed.
More than 81 per cent of teenagers aged 12-15 have had one vaccine dose, and 76.8 per cent have had both.
The emergence of the new variant has also seen the number of people getting booster shots increase by 40 per cent, Mr Hazzard said.