Nearly 40 people were facing fines of more than $5,000 as Northern Territory Police investigated whether they breached an order to self-isolate while they awaited coronavirus test results.
Police said the potential breaches all occurred after Greater Melbourne was declared a coronavirus hotspot late last week.
At the time, anyone who had arrived in the NT from February 7 was ordered to self-isolate until they received a negative test result.
Police and health officials have conducted 270 compliance checks since Friday and say 38 potential breaches are under investigation.
One person, a 31-year-old man, has already been handed a $5,506 fine for leaving his self-isolation address on Sunday.
He had arrived in the NT from Melbourne last Thursday.
Over the weekend, a 20-year-old woman who returned from Melbourne on the same date was also fined after admitting she left her home to get takeaway.
Acting Commander Scott Pollock said authorities were unable to contact the 38 people suspected of not self-isolating during their routine compliance checks.
"These are currently under investigation and further infringements will now be issued," he said.
"If you are under a direction to self-isolate, compliance officers will come knocking at your door.
Chief Minister Michael Gunner said more than 1,000 people would be affected by the self-isolation directive when it was announced.NT Health Minister Natasha Fyles on Monday said the potential breaches were "disappointing" and the people involved may have put the community at risk.
"We've seen the large majority of Territorians do the correct thing and abide by the rules," she said.
"But it is disappointing from time to time when you do see people not listen to the advice, and potentially put our community at threat."
According to NT Police, 169 people had been fined for breaching Chief Health Officer directions at the end of January.
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