Health Minister Natasha Fyles says the positive and negative test results were sent on Wednesday night during a computer system upgrade.
"It appears to have put a glitch in our system that thousands, around 8000 text messages, automated messages, have gone out to people that have previously had COVID tests," Ms Fyles said on Thursday.
"I received one. It has the dates and mine was from a test back in August last year."
It means Territorians who had previously been tested for the virus were sent repeat messages containing their historical test results.
Ms Fyles apologised to the affected people and said the technical issue had been fixed.
"We have seen many text messages go out informing people of a test result," she said.
"If you did get a text message saying you're positive and you haven't had a recent test, please look at that date just to clarify."
It comes as the NT reported 655 new cases and one death.
Forty-nine people are in hospital and one person is in intensive care.
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