They were on Jetstar JQ258. More information for those who were on the flight will be available on the Te Whatu Ora website from tomorrow.
Medical Officer of Health for the Northern Region Jay Harrower said the person, who lives in Northland, attended a week-long National Shakespeare Schools Production at Scots College.
The students they were in contact with then travelled to other parts of the country.
"We are asking those people who were at the Scots College event to isolate until they have been contacted by public health. Everyone on the flight should get vaccinated if they are not immune or if they are unsure. Those at high risk will be contacted by public health services in the next few days," Dr Harrower said.
"We are asking New Zealanders to be alert to the symptoms or get vaccinated if they haven't already."
Measles was very contagious among people who were not immune, he said.
"The first symptoms of measles include a fever, cough, runny nose, and sore and watery pink eyes. This is followed by a blotchy rash.
"We would like to remind people to be up to date with the immunisation. If you are unsure whether you have had one or two doses of MMR, get vaccinated as there is no additional risk in getting an extra dose," Dr Harrower said.
Te Whatu Ora is working to identify places and people who may have come into contact with the individual.
There will also be a full list of exposure events once Public Health Services has identified them all.
Te Aka Whai Ora Māori Health Authority chief medical officer Dr Rawiri McKree Jansen said this was a "serious wake-up call about the high risk of measles, particularly to our pēpi, tamariki and rangatahi".
He said immunisation was the best protection against measles.
"We urge everyone to be aware of the symptoms of measles and to call your healthcare provider if you suspect anyone in your whānau has measles."
