"People who are not immune may start experiencing symptoms over the next week," Poynter said.
New Zealanders over 50 years are considered to be immune as the virus circulated widely when they were children.
Measles is a highly infectious and potentially deadly disease that spreads easily through the air via coughing and sneezing.
If you do start to develop symptoms that could be measles, also contact your doctor. Be sure to call ahead to prevent potentially infecting others in the waiting room.
If you were on the flight and are unsure whether you're immune to measles, talk to your doctor or call Healthline on 0800 611 116 for advice.
At least 298 people have been infected with measles in Auckland during the outbreak this year.
Poynter said the most effective way of bringing the outbreak to an end is to have as many people as possible aged between 12 months and 50 years with at least one measles, mumps and rubella (MMR) vaccination.
"In particular, older teenagers and people in their 20s and 30s need to check that they have had an MMR, because we know that vaccination rates were not as high when these people were younger," Poynter said.
He said 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.
For more information about measles, visit the measles page on the ARPHS website or the Ministry of Health website.