The flight landed at Auckland Airport at 4.20am on July 4. Anyone who was in the airport arrivals area around that time should also watch out for symptoms of the highly infectious disease, ARPHS clinical director Dr Julia Peters said.
New Zealand is in the middle of a measles outbreak, with 280 cases confirmed this year - 164 of those in Auckland.
All of the virus strains circulating in New Zealand have come from people arriving from overseas.
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It takes 7-14 days to start experiencing symptoms, including high fever, runny nose, cough and sore red eyes, Peters said.
"A few days later a rash starts on the face and neck, then spreads to the rest of the body."
Those exposed to the passenger should watch out for symptoms from Thursday, July 11.
"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.
Measles is an airborne disease that spreads easily through the air via coughing and sneezing.
Anyone on the flight who is unsure if they have immunity should talk to their doctor or call Healthline on 0800 611 116 for advice.
If you do start to develop symptoms of measles, contact your doctor - but be sure to call ahead to prevent potentially infecting others in the waiting room.
Vaccination with the measles, mumps, rubella vaccine (MMR) offers the best protection against measles. One dose will prevent measles in 95 per cent of people, while having two doses will protect 99 per cent of people who have the vaccine, the ARPHS said.