The person is likely to have contracted the virus during his two-week quarantine in a Perth hotel, health officials said, adding genomic sequencing was underway to trace the source.
All passengers on a flight from Perth to Melbourne have been asked to self-isolate as the infected person on Wednesday travelled to his home in Melbourne after finishing his mandatory isolation, Victoria state Health Minister Martin Foley said.
"This is an important and I think timely reminder to all of us, that this global pandemic is not over," Foley told reporters in Melbourne.
Western Australia and New South Wales states are currently investigating into cases of travelers in quarantine contracting the virus from infected guests staying in nearby rooms.
"The hotel quarantine system, despite all of its improvements, has to face increasingly complex variants of concern," Foley said.
To tackle the risks of highly contagious variants of the virus spreading, Australia on Thursday tightened its border controls by reducing the number of travelers from India and other virus hotspots.
Having closed its borders more than a year ago, Australia lets mostly citizens and permanent-residents return from abroad. Returned travelers, except from New Zealand, have to undergo two weeks of mandatory hotel quarantine at their own expense.
The hotel quarantine system has helped Australia to keep its COVID-19 numbers relatively low compared with other developed countries, with just over 29,500 cases and 910 deaths.