McElnay said as we'd seen around the world, Covid 19 could be fatal for elderly people with underlying health conditions.
The woman was one of the residents from the Rosewood rest home moved earlier in the week.
She had a number of age-related health conditions and because of level 4, her family wasn't able to visit her or be with her before she passed away in hospital.
Meanwhile there are now 24 cases in Northland - 22 confirmed cases and two probable cases - a rise of 4 cases in 24 hours.
There are currently no confirmed cases of Covid-19 in Northland hospitals, with 18 of the cases self-isolating in the community and six have now fully recovered.
Fourteen of the new cases announced today are linked to existing clusters. In total, 373 people have recovered - an increase of 56 on yesterday. The total number of cases in New Zealand is 1283.
There are 16 people in hospital. Four are in ICU, Wellington, Waitemata, Waikato and Southern - two of whom are in a critical condition.
• Covid19.govt.nz: The Government's official Covid-19 advisory website
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There continues to be a strong but declining link to overseas travel but with a growing link to confirmed cases. There are 12 clusters of more than 10 people.
If New Zealand hadn't been in level 4 lockdown, the spread from the Bluff cluster could have been much worse, McElnay said.
The rise in cases today confirmed New Zealand couldn't be "too complacent" in our response to the virus, she said.
Strict quarantine for all arrivals at the border will be in place indefinitely and remains a key measure in what the Prime Minister is calling the "marathon" fight to eliminate Covid-19.
During her press conference yesterday, Jacinda Ardern urged New Zealanders to remain vigilant and lockdown-compliant as they headed into Easter, warning not to let up.