Health officials in Queensland believe 19 community contacts and 40 staff at a hospital have been exposed to the man, who recently returned to Australia from Africa.
The patient was diagnosed with a rare strain of Clade 1 mpox after he presented to Logan Hospital, south of Brisbane.
But he was not contagious during his journey to Australia, health officials say.
"Those close contacts that he has been in contact, including at the emergency ward and in other locations, are being contact traced right now and identified at this stage," Health Minister Tim Nicholls said on Sunday.
"At the moment his family are asymptomatic, that is, they're not showing any signs of the Clade 1 mpox, but they are isolating."
The man's family includes children at high school, primary school and child care centres and those institutions are being identified, Mr Nicholls said.
Health officials do not expect the number of community contacts to increase, but the number of hospital contacts could grow.
Mpox is a viral infection that typically displays mild symptoms of fever, headache, muscle aches, swollen lymph nodes or fatigue, followed by a skin rash or lesions.
"The contagion window we define as being four days before the onset of symptoms, until after the skin lesions have crusted over," Dr Geoffrey Playford from Metro South Hospital Service said.
There have been 135 cases of Clade 2 mpox in Queensland over the past year.
Only once before has Clade 1 been detected in Australia, after a returning traveller tested positive for the virus in NSW in May.
The disease does not easily spread between people and mostly occurs through very close or intimate contact with someone infected.
Groups at higher risk of infection include sexually active gay, bisexual or other men who have sex with men and their partners.
People travelling to areas where the Clave 1 variant is circulating - particularly Central Africa and adjacent countries - and who are likely to have sexual contact are recommended to have a vaccine before departing.
Health authorities say vaccinations for pre- and post-exposure to the disease are effective and are available for free through sexual health clinics and general practitioners.
Two doses of vaccine are needed for optimal protection.
The mpox outbreak was declared a public health emergency of international concern by the World Health Organisation in August 2024.
It was first detected in Australia in 2022, with the number of cases spiking to more than 1400 in 2024, according to Australia's National Notifiable Disease Surveillance System.
8°C