Dr Peters urged any passengers from the flight who felt unwell to call their doctor before visiting.
"It is vitally important to call first because measles is a highly infectious airborne disease, and people with measles can easily infect others in doctors' waiting rooms."
She said those passengers who sat nearest the infected person were at the highest risk of infection, and public health services would try to contact them.
"We want all passengers to be aware and vigilant," Ms Peters said.
The initial symptoms of measles include a fever, running nose, cough and sore eyes.
After about a week, a raised red rash spreads over the body lasting several days.
Ms Peters said measles was a serious illness and there was no treatment.
"The only way to avoid catching measles is to have had two measles vaccinations, at 15 months and four years."