Restrictions are also in place for international students and skilled migrants who have been in any of the nine countries in the past two weeks.
All flights from the nine countries have been suspended for 14 days "as a matter of precaution".
The variant, which originated in South Africa, is still an enigma to global epidemiologists, but the UN health agency said in a statement the variant had a "large number of mutations, some of which are very concerning".
"The variant has been detected at faster rates than previous surges in infection, suggesting that this variant may have a growth advantage," the statement said.
Hunt said he wanted to emphasise how "well-placed" Australia was to fight the Omicron challenge.
"(But) on the basis of medical advice, the Australian Government ill be implementing additional precautionary border security measures in order to protect Australians while more is learnt about the nature and impact of the Omicron variant of concern," he said.
"There are currently no known cases of the Omicron variant in Australia."
Australia does not receive any direct flights from South Africa, however, repatriation flights have arrived into the Howard Springs quarantine facility.
There are currently 20 people in that facility who arrived from South Africa last week, but the one positive Covid case is not the Omicron strain.
Currently Australians arriving into Victoria, NSW and the ACT from overseas do not need to quarantine.
Professor Kelly said he knew there were a "small number" of travellers who had arrived in those states who authorities were trying to track down.
Queensland's deputy chief health officer told journalists on Saturday that it was still "too early to panic" about the Omicron variant, but the AHPPC – the group of federal, state and territory chief health officers – would meet later in the day.
"It's too early. We need to get more information before we act," he said.
NSW Health Minister Brad Hazzard said he had been briefed several times on the new variant.
He urged anyone who has been to South Africa in the past fortnight to be "very, very aware of their symptoms".
But he also said people who have visited other countries could potentially spread the variant.
"We're still keen to keep the balance in NSW," Hazzard told reporters.
"It's important that we have our economy open, important to mental health, important for a whole range of reasons."
NSW Premier Dominic Perrottet said he had made no decision to change the state's pandemic rules but added the "road map" could be tweaked if necessary.
"From time to time there will need to be targeted restrictions," he said.
"Any changes that need to be made in relation to incoming travellers from overseas, who have been to South Africa or those related countries, we will ensure the appropriate steps are taken to keep the community safe."
The United Kingdom closed its borders to southern Africa, followed by other countries in Europe, the United States and Canada.
The first case of the variant detected in Europe was announced in Belgium late on Friday night Australian time.
