She and her partner are in isolation at home. Her two children, who attend Westlake Boys' and Westlake Girls' High Schools, are also staying home although they are not sick.
Her partner has shown symptoms of the virus and has been tested, with results due back today.
Air New Zealand cabin crew from the three flights would be stood down from duty and would be self-isolating for 14 days at home as a precaution, a spokeswoman from the airline said.
"Our employees are being updated regularly on the situation as it evolves and we are reminding them of the best ways to protect themselves from viral respiratory infections."
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The woman and her partner had been in northern Italy, where there is an outbreak of Covid-19.
The first leg of her journey home was from Milan to Singapore's Changi Airport on a Singapore Airlines flight, according to Singaporean media outlet the Straits Times.
SIA pilots and crew from that flight had also been stood down and asked to monitor their health at home, the Straits Times said.
Public health staff are making "very good progress" contacting those who had been on the flights, Minister of Health Dr David Clark told the AM show this morning.
Close contacts - those who are within one metre of an infected person for 15 minutes or more - are considered most at risk of contracting the virus. On flights, this means people sitting in the same row, two rows in front and two rows behind.
Anyone who was on the flights and is concerned or would like information should contact the Healthline number 0800 358 5453.
