In a statement, the Ministry said the person works at the facility and is not a returnee, so are considered a community case.
The case was reported to the Ministry this afternoon.
It said the person had been tested regularly. They were most recently swabbed on 3 November and returned a negative test the next day.
But the staff member then developed symptoms on 5 November and was tested again that day. That test has returned a positive result.
Contacts of the worker are being traced, isolated and tested.
The person visited Auckland's Mezze Bar and a Queen St bottle shop on November 5 and people who visited the businesses are being asked to watch for symptoms.
The case was infectious while in the restaurant that day for a brunch.
Anyone at the Mezze Bar between 11am and 1pm on 5 November is considered a casual contact, should watch for symptoms and get tested if they feel unwell.
Auckland Regional Public Health Service spokesperson said the person dined alone, and there have been no close contacts identified at the restaurant.
They also visited the Liquor.Com bottle shop at 456 Queen St for 15 minutes at about 1.30 pm. Anyone who visited between 1pm and 2pm on that day are also casual contacts and should watch for symptoms.
The case's close contacts at home and at work have been identified, and are self-isolating and getting tested.