Australia has joined a growing list of nations affected by the rare tropical illness, with the Victorian health department confirming the case on Friday afternoon.
The traveller, a man in his 30s, developed mild symptoms before landing in Melbourne on May 16 and sought immediate medical attention.
A general practitioner referred him for testing, which came back positive, and he was placed in isolation at The Alfred on Thursday.
Monkeypox does not easily spread between people, Victoria's Chief Health Officer Brett Sutton says.
"There are few close contacts that have been identified, obviously the GP is one of them," he told reporters on Friday.
Contact tracing is also underway for passengers seated nearby the man on board flights EY10 from London to Abu Dhabi on May 14 and flight EY462 from Abu Dhabi to Melbourne on May 16.
They are being asked to monitor for symptoms and isolate only if they develop symptoms.
NSW Health has also detected a possible case of monkeypox in a man in his 40s who recently returned from Europe.
The man developed a mild illness several days after returning from Europe, with his GP assessing his symptoms to be similar to the disease.
Confirmation testing is under way and the man and a household contact are isolating at home, NSW Health said.
Australia joins Italy, Sweden, the United Kingdom, Spain, Portugal and the United States as nations dealing with outbreaks.
Monkeypox occurs mainly in central and western Africa, often close to tropical rainforests, and is considered endemic in the Democratic Republic of Congo, where it was first discovered in humans in 1970.
The illness can be transmitted from person to person through air droplets, close bodily contact or sharing contaminated linens or objects.
Four countries in Africa - Cameroon, Central African Republic, Democratic Republic of Congo and Nigeria - have reported cases of monkeypox in 2022.
NSW Chief Health Officer Kerry Chant said monkeypox is a rare virus that did not spread easily between people.
"The infection is usually a mild illness and most people recover within a few weeks," she said.
The general public and health clinics should be aware and have unusual skin rashes examined by specialist staff, the World Health Organisation said.
The WHO also called for vigorous contact tracing around the spate of cases.
Prime Minister Scott Morrison said state health authorities were closely monitoring the situation.
"The advice I have is that it is a far less contagious condition than obviously COVID and things of that nature," Mr Morrison told reporters in Perth.
"We should be taking this seriously (but) at the same time I would say that no one should be alarmed at this point. We've got the best health authorities in the world."
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