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The message was sent to people who have tested positive for the virus in the last 10 days, meaning the text was a duplicate of advice they had already received.
The Covid-19 Response Minister's office said Ayesha Verrall was aware of the incident and has been assured by the Ministry it was the result of a glitch.
An uploading error on Friday afternoon and through into Saturday morning meant people were sent repeat text messages mistakenly telling them they had returned a positive test for the virus.
"The duplicate text again told the recipient they'd tested positive for Covid-19 and gave the standard advice about isolating, asking them to fill in the contact tracing form and where to find information, support, and healthcare advice," the Ministry admitted tonight in a Twitter post.
The Ministry's contact tracing team discovered the problem early on Saturday morning and the error was fixed that day.
Text messages have been sent to all those affected to clarify the error, apologise and provide a phone number should people require further information or support, the Ministry said.
The phone line will be available today until 9pm and again from tomorrow morning.
The Ministry reported 4024 new community cases of Covid-19 in New Zealand today.
There were also a further nine Covid-related deaths, including two people from the Auckland region, two from the Bay of Plenty, two from Wellington, two from Canterbury and one from South Canterbury.
There are 391 people in hospital with the virus, including three in intensive care.