This year's outbreaks are already the worst since 2011 when 597 people contracted the disease.
Auckland Regional Public Health Service clinical director Dr Julia Peters said anyone who may have been in contact with the person in the departure area of Auckland Airport's domestic terminal around the time of the flight should watch for signs of the measles, as should anyone who was on the flight or in the arrivals area in New Plymouth.
"It can take 7-14 days to start experiencing symptoms and you are most at risk if you're not immune to measles, either because you haven't been vaccinated or you haven't had the disease previously," Peters said.
Symptoms include a high fever, runny nose, cough and sore red eyes. A few days later a rash starts on the face and neck, before spreading to the rest of the body.
Measles is an airborne disease that spreads easily through the air via coughing and sneezing.
Public health officials were made aware of the case after the infected person sought medical attention in New Plymouth.
Peters said people should call their doctor or Healthline, on 0800 611 116, if they were on the flight and unsure whether they were immune to measles.
She said those who started to develop symptom should call the doctor or hospital before going in so as not to spread the disease to others in the waiting room.
Vaccination with the measles, mumps and rubella vaccine (MMR) offered the best protection against measles, she said. One dose would prevent measles in 95 per cent of people, while the recommended two doses would protect 99 per cent of people who have the vaccine.
For more information about measles, visit Auckland Regional Public Health Service's measles page or the Ministry of Health website.