Geoscience Australia says the earthquake was detected around Mansfield in Victoria's north-east around 9:15am and was 10-kilometres deep.
The quake was felt 190 kilometres away in Melbourne as well as in regional Victoria, Sydney, regional New South Wales, the ACT, Adelaide and Launceston in Tasmania.
There are reports emerging of significant damage in some parts of Victoria.
Apartment buildings are being evacuated in inner Melbourne, where damage to streets and roads is being posted to social media.
Ross, 60, who lives on the Bellarine Peninsula told ABC Radio Melbourne it was the biggest earthquake he had ever experienced.
"We've just moved into a round earth house on a concrete slab and the whole thing just rock and rolled and the water in the swimming pool went sloshing backwards and forwards," he said.
"I couldn't believe it."
Margot in Moonee Ponds said at first she thought her daughter was pranking her when her whole house began shaking.
"It was quite intense," she said.
"My chair was shaking… everything in the room was rattling and clinking together."
Expert says aftershocks could continue for months
Seismology Research Centre head Adam Pascale said the epicentre of the quake was north-east of Aberfeldy and the Thomson Dam in the Alpine National Park.
"We are still refining it, but we think it's a mag-5.8 potentially at this point in Gippsland," he told ABC Radio Gippsland.
"It shook here in the northern suburbs of Melbourne for about 15-20 seconds so it's quite a significant earthquake."
Mr Pascale warned there could be aftershocks to come and they could continue for months.
"There is a small likelihood that there could be a larger event but we'll see as we go," he said.
"The main things for people to remember is if they do start to feel some shaking. There's usually a primary and a secondary wave.
"The primary wave will give you a few seconds to get under a table and hold on."
Photo supplied ABC News