The woman's family members are the man and toddler who completed managed isolation at the Pullman Auckland hotel in mid-January.
The ministry said the woman had no close contacts to follow up due to being in self-isolation and therefore the public health risk was considered to be low.
Today's case brings the number of confirmed cases since the outbreak began almost a year ago to 1959.
Plea to Kiwis over Waitangi weekend
Today, the director-general of health Dr Ashley Bloomfield made a special appeal to New Zealanders ahead of the Waitangi Day celebrations.
"If you're out and about over Waitangi weekend, it's more important than ever that you keep a record of where you've been," said Bloomfield.
"We continue to strongly encourage people to continue to scan using the NZ Covid tracer app and turn on bluetooth. The more we all scan, the safer we'll all be. Scanning helps our contact tracers to quickly find and alert any potential close and casual contacts of people who have tested positive for Covid-19."
The ministry said 4875 tests were processed yesterday. The seven-day rolling average up to yesterday was 4710 tests.
There have now been 1,551,707 tests processed by laboratories to date.