They returned an initial negative PCR test on Saturday before developing symptoms on Monday, when they returned a positive test result.
The source of infection remains under investigation and all other passengers on the flight are being followed up to ensure they have been tested, in line with current requirements for overseas arrivals.
The department is also investigating likely Omicron cases detected in the cities of Casey and Brimbank.
The two cases have returned results with S gene dropout - a signature of the Omicron variant.
"Household contacts of these cases have also tested positive and whole genome sequencing is underway to confirm whether these represent the Omicron variant," the department said.
"None of these cases are linked to international travel and their source of acquisition is under investigation."
Several contacts of the two cases have been identified and told to quarantine for 14 days, while lower risk contacts have been instructed to get tested and isolate until they receive a negative result.
Further tracing is ongoing and is likely to produce more contacts.
The department said their advice may change if genomic sequencing shows the cases are not infected with Omicron.
The variant, which was first observed in South Africa, has already been detected in NSW, the ACT and the NT.
It comes as Victoria reported 1312 new COVID-19 infections and a further five deaths.
It brings the total number of active cases in the state to 11,331, down from 13,050 on Tuesday.
There are 303 people battling the virus in hospital, 97 of whom are in intensive care and 27 requiring ventilation. The seven-day hospitalisation average sits at 297.
Testers processed 79,490 results on Tuesday, while 3858 people were vaccinated in state-run hubs.
More than 91 per cent of Victorians over 12 are fully vaccinated.
Omicron scare on Sydney Harbour cruise
There are fears a Sydney Harbour boat cruise could turn into a super spreader event after five party-goers tested positive to COVID-19, with two likely to have the highly contagious Omicron variant.
NSW Health says genome sequencing is underway to confirm if any of the five confirmed cases have Omicron but preliminary results indicate two are likely to have it.
All cases are isolating at home.
Authorities are now urgently trying to contact about 140 people who signed in with a QR code before boarding the boat on Friday, which left King Street Wharf 9 at 7.30pm and returned about 11pm.
Anyone who was on board, and everyone in their households, is being urged to immediately get tested and isolate.
The cruise was jointly marketed as 'Flow Fridays - 90s Themed Boat Party' and 'Freaky Sunday Afrovibe: The Last Dance'.
Thirty-one cases of the Omicron coronavirus variant have been registered in NSW.
A growing cluster linked to a climbing gym in Sydney's southwest and two schools has increased to 20, with more cases expected.
Chief Health Officer Kerry Chant said the original source was believed to be a traveller who had been in Nigeria and arrived in Sydney from Doha on flight QR908 on 23 November.
"It's expected that the numbers linked to this cluster will rise as further results are confirmed over the coming days," she said on Tuesday.
NSW Health is consulting widely in an effort to determine how contagious the new variant is and how it is transmitted compared with other variants.
"We are working with our international counterparts to rapidly gain a better understanding about the nature of this new variant," Dr Chant said.
"We are also working to understand the severity of the new variant and importantly how effective vaccines are at offering protections against severe disease."
The state recorded 403 new COVID-19 cases from 92,566 tests in the 24 hours to 8pm on Tuesday.