The 23-year-old allegedly made a false declaration on Monday at the Queensland border, saying he'd been in Mt Isa for the 28 days before he entered the NT.
The man is also accused of stealing petrol from service stations along the Barkly and Stuart Highways before reaching Darwin.
The fuel thefts were reported to NT police and investigating officers discovered the man had been denied entry to Queensland from NSW at a checkpoint on the Gold Coast on November 12.
NT police spoke with the man's relatives and he handed himself in to officers on Tuesday.
He was then placed in quarantine at the Centre for National Resilience at Howard Springs where he allegedly refused to wear a face mask and declared his intention to leave the facility.
Officers re-arrested the man and he has since been charged with reckless endangerment, two counts of contravening an emergency declaration and three counts of stealing.
He was refused bail and placed on remand at Holtze Prison, where he will complete quarantine in isolation.
Meanwhile, genomic testing has confirmed the territory's current outbreak was triggered by an infected woman who also illegally entered the NT.
The 21-year-old lied on her border entry form late last month before travelling from Cairns to Darwin after visiting Victoria, where she contracted the virus.
She infected a man she spent time with in Darwin and the virus spread to two others in Katherine before authorities declared they had control of the outbreak on November 9.
But that was short-lived, with the same strain of virus now found to be responsible for the current cluster, which has grown to 19 cases since Monday.
It started when a 30-year-old woman and a 43-year-old man from Katherine, 320km south of Darwin, became infected.
The woman was unvaccinated and travelled from Katherine to Robinson River - 1000km southeast of Darwin - where she tested positive, the first case reported in a remote NT Aboriginal community.
Nine new cases were detected in Katherine on Tuesday, including a 71-year-old man and a 65-year-old woman who was admitted to Royal Darwin Hospital.
Eight new cases were reported on Wednesday, with five infections diagnosed in Robinson River, including a three-week-old girl.
All those infected are Indigenous Territorians.
No new cases were recorded on Thursday but Chief Minister Michael Gunner warned the crisis was not over.
"This is good news, but it is not a day to get ahead of ourselves," he said.
"This is Delta, it's in large vulnerable households. We're not out of the woods."
Health teams are now concentrating on finding the missing links between the two clusters, with NT Health saying it now knows the virus was circulating in Katherine from November 4 to 13.
Greater Katherine and Robinson River are currently under a seven-day lockdown order, which is scheduled to end late Monday.
Mr Gunner is expected to update the community on the outbreak about midday on Friday.
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