The unvaccinated woman in her 70s from Binjari Aboriginal community died about 11.30pm on Thursday in Royal Darwin Hospital.
"This is a very hard day," Chief Minister Michel Gunner told reporters on Friday.
"This is the news we never wanted to give.
"While we are the last place in Australia to have one of our own succumb to COVID, it is very unlikely to be the last time we have to deliver such news."
Mr Gunner said the woman was admitted to hospital on November 20 and had underlying health issues.
There are 60 cases in the territory's current outbreak. The majority are Indigenous Territorians.
The fatality comes a day after the virus was detected in another remote community, with a 45-year-old man diagnosed in Lajamanu, 900km northwest of Alice Springs, near the Western Australia border.
Mr Gunner said the man contracted the virus after travelling 600km to Katherine to get his second vaccine dose on November 15.
Lajamanu is the third Aboriginal community to record an infection.
The outbreak started when an infected woman illegally entered the NT in late October.
The 21-year-old lied on her border entry form before travelling from Cairns to Darwin after visiting Victoria, where she contracted the virus.
She infected a man in Darwin before the virus spread to Katherine, then the Aboriginal communities of Robinson River - 1000km southeast of Darwin - Binjari and Lajamanu.
"Unfortunately this death does apparently have links to a breach of health officer directions," NT Police Commissioner Jamie Chalker said.
"It appears to be the seed that started the spread of COVID within the NT and as such Major Crime are now undertaking an investigation."
Nineteen people from Binjari - 330km south of Darwin - have been diagnosed with the virus since the first cases were detected in the community of about 200 on November 20.
Dozens of infected residents and close contacts have been moved to The Centre for National Resilience quarantine facility at Howard Springs near Darwin.
The health response to limit the outbreak has tested all those involved as the virus spread to remote communities where residents often live in overcrowded housing and temperatures can climb above 40C.
Meanwhile, two travellers to the NT from Victoria and South Australia - unrelated to the current cluster - have tested positive for the virus.
They have been moved into the Howard Springs quarantine facility with their families.
Across the NT, 88 per cent of people over the age of 16 have had their first vaccine dose and 78 per cent are fully vaccinated.
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