The ministry website said the computer glitch had been corrected.
A similar glitch last month forced the ministry to apologise to 6000 people after it incorrectly notified them they had tested positive and needed to isolate.
The message was sent to people who had tested positive for the virus in the past 10 days, meaning the text was a duplicate of advice they had already received.
Text messages were sent to all those affected to clarify the error, apologised and provided a phone number should people require further information or support.
The ministry reported a further 23 Covid-related deaths today. Eighteen of the deaths occurred in July. Four others were from May and June.
There were 587 people in hospital with the virus, including nine in intensive care.
Of today's 23 deaths, seven people were from the Auckland region, one each from Waikato, Lakes, Bay of Plenty, Hawkes Bay, Taranaki, Tairawhiti, Whanganui and MidCentral, two were from the Wellington region, four were from Canterbury/West Coast, and two from Southern.
One was aged in their 60s, three were in their 70s, 13 were in their 80s, and six were aged over 90. Of these people, nine were women and 14 were men.
One death from January last year was now being reported by the ministry as the cause of death assessment had been completed.
Today's reported deaths took the total number of publicly reported deaths with Covid to 1651.
The breakdown of today's 587 Covid hospitalisations is: Northland: 13; Waitematā: 128; Counties Manukau: 38; Auckland: 35; Waikato: 57; Bay of Plenty: 32; Lakes: 14; Hawke's Bay: 20; MidCentral: 18; Whanganui: 6; Taranaki: 11; Tairawhiti: 2; Wairarapa: 4; Capital and Coast and Hutt Valley: 60; Nelson Marlborough: 13; Canterbury and West Coast: 90; South Canterbury: 15; Southern: 31.
There are nine Covid patients in ICU or HDU. The average age of Covid hospitalisations was 66.
