The 22-year-old man flew in from Pakistan via Thailand 11 days ago, the Sydney Morning Herald reported.
The man, who is now in a hospital isolation unit, is a student living in Melbourne who had just completed a vacation in his home country, said the Australian government's Chief Medical Officer John Horvath.
The man had been on a Thai Airlines flight to Melbourne from Bangkok.
Health authorities are trying to contact all 249 passengers on that plane as a precaution.
Dr Horvath, however, said there was only a low risk that others had contracted the disease.
Polio, or poliomyelitis, invades the nervous system, and can cause paralysis in a matter of hours. Children under three are most at risk from the virus.
Initial symptoms are fever, fatigue, headache, vomiting, stiffness in the neck and pain in the limbs. One in 200 infections leads to irreversible paralysis, usually in the legs.
Dr Horvath said Australia's last known polio case was reported in 1986 and the country and the rest of the western Pacific region had been certified polio-free in 2000.
"We knew it was sporadic in the area of Pakistan, India and other areas, where we do get some travellers going to and from," he said.
"Our health authorities and our doctors always have kept an eye out in case something like this did happen."
