The earthquake took place about 09:15 local time (23:15 GMT) 38 kilometers south of Mount Buller in the country's south east, the U.S Geological Survey said.
The tremor was also felt in neighboring South Australia and New South Wales (NSW), according to local sources.
“At this stage, we have had no reports of serious injuries or worse. And, that is, that is very good news, and we hope that that good news will continue,” Prime Minister Scott Morrison said.
“It can be a very, very disturbing event, for an earthquake of this nature. They are not, they are very rare events in Australia. And, and as a result, I'm sure people would have been quite distressed and disturbed by that, particularly in the most immediate area affected,” he added.