The powerful 7.6-magnitude quake struck in the Banda Sea near the Tanimbar Islands, east of Timor-Leste, about 3am local time on Tuesday, at a depth of about 90km.
A tremor was felt hundreds of kilometres away in Darwin, where many residents feared for their lives and evacuated apartment buildings.
Olympian and former senator Nova Peris said she had experienced six or seven tremors while living in Darwin, but she had never felt anything like the early-morning quake.
"It felt like a steam train coming a million miles an hour," she told Ten News.
"I just sat there with the fear, just frozen because the house was just shaking so violently."
Videos uploaded to social media show walls and homewares in kitchens shaking during the tremor, which some residents say lasted three minutes.
It was followed several minutes later by a nearby 5.4-magnitude aftershock.
The Joint Australian Tsunami Warning Centre assessed there was no tsunami threat to the Australian mainland, islands or territories.
Darwin resident Tracey Wedel feared her house would collapse due to the violent shaking.
"Everything was banging and shaking, the doors were shaking, I thought the house was going to fall apart," she told AAP.
"It was literally the strongest (earthquake) I've ever felt. Dogs up the street were barking and it went on for about two and a half minutes."
Amy Hetherington moved to Darwin 10 years ago and said it was the biggest earthquake she'd felt during that time.
"We're in a two-storey troppo house so you could feel the place swaying," she told AAP.
"Hubby and I got up and watched the things on the shelves and pictures, worried they might fall down. But really so lucky."
Northern Territory Chief Minister Natasha Fyles was also shaken awake.
"Suspect a few of us are going to need a coffee (or four) to get going later this morning after that shock," she said on social media.
More than 3000 people in northern Australia reported feeling the quake to Geosciences Australia.
"It was really strong and just kept going and going. Up on the 10th floor of my apartment building you could feel the whole building moving," resident Ben Tuffnell told AAP.
"I bolted downstairs and about a dozen people were down there, confused."
The tremor was also felt from Nhulunbuy in northeast Arnhem Land down to Tennant Creek in the centre of the Northern Territory, which Geoscience Australia senior duty seismologist Tanja Pejic described as significant.
"It's quite possible that we will see (more) aftershocks along those magnitudes of maybe five or larger that might still be felt, although I suspect it wouldn't be felt as widely as the 7.6 earthquake," she told AAP.
There were no injuries or damage reported from the earthquake, according to NT Police, Fire and Emergency Services.
Business Minister Paul Kirby said assessments would be carried out on any reported damage.
Indonesian authorities have said early reports indicated light to medium damage to buildings on the islands.
News website Liputan6.com reported houses in Saumlaki town in Yamdena island were badly damaged.
The country issued a tsunami warning for almost three hours after the quake, but no significant changes in sea level were recorded.
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