The rare quake shook buildings, knocked down walls and sent panicked Melbourne residents running into the streets (AFP/William WEST)
Geoscience Australia reported the initial quake was followed by a series of four smaller ones, ranging from magnitude 2.5 to 4.1.
Sandiford said Australians should expect "many hundreds of aftershocks, most below human sensitivity threshold, but probably a dozen or more that will be felt at least nearby".
The quake "would have caused many billions of dollars in damage had it been under Melbourne", he added.
The mayor of Mansfield, near the quake epicentre, said there was no damage in the small town but it had taken residents by surprise.
"I was sitting down at work at my desk and I needed to run outside. It took me a while to work out what it was," Mark Holcombe told public broadcaster ABC.
"We don't have earthquakes that I am aware of -- none of the locals I spoke to this morning had that experience with earthquakes here before -- so it is one right out of left field."
Emergency services said they had received calls for help as far away as Dubbo, about 700 kilometres (435 miles) from the quake epicentre, with fire and rescue crews dispatched to help.
Prime Minister Scott Morrison, speaking from New York, said there were no initial reports of injuries.
"It can be a very, very disturbing event for an earthquake of this nature," he said. "They are very rare events in Australia."
Recovery efforts may be complicated by the ongoing pandemic lockdown and ongoing protests.
Hundreds of demonstrators wearing work boots and hi-visibility jackets again rampaged through central Melbourne Wednesday in protest against vaccine requirements for construction workers.
Police on Tuesday fired pepper spray, foam baton rounds and rubber ball grenades to disperse the crowd and warned further protests would "not be tolerated".
Important Update: MetroExpress Service ONLY Available via Karwa Taxi App from June 24
WhatsApp lets users hide profile photo, last seen from specific people
Box Office: Pixar's 'Lightyear' Underwhelms With $51 Million Debut as 'Jurassic World' Stays No. 1
Qatar ranks number one most peaceful country in Arab World