Paediatricians are worried about the scare - the third this year - in the face of falling vaccination rates.
Te Whatu Ora had been urgently contacting 44 people who were on a Jakarta to Sydney flight on 15 February, and who then travelled to New Zealand.
It had reached 31 who were either immune or overseas.
Eight more had been contacted but have yet to be interviewed by public health staff, while they are still looking for five more.
Anyone who had contracted the disease would likely be infectious now.
There has been one confirmed case of measles in the country this year, and two situations where New Zealand passengers were potentially exposed on international flights.
The Paediatric Society was worried about falling rates in very young children and urging parents to check their children had all the vaccinations they were supposed to.
Only 77 percent of children aged 18 months are up to date with their scheduled childhood vaccinations.
That fell to 47 percent for Māori children and 56 percent for Pacific children.
Auckland paediatrician and spokesperson for the Paediatric Society Owen Sinclair said the rates were a real worry.
"It really puts those populations at a great risk of pretty serious disease.
"Measles can make you very sick and it can have some very poor outcomes and even fatal outcomes as we saw in Samoa.
"That's what we're worried about... the threat to our precious tamariki."
In New Zealand's last outbreak, in 2019, 700 people were hospitalised
It was likely the disease was spread from here to Samoa, where 83 people died, most of them children.
Dr Sinclair said more focus needed to go into making sure vulnerable communities had access to vaccination.
A campaign to reach another under-vaccinated groups, teens and adults in their 20s had stalled in the Covid pandemic.
Te Whatu Ora's chair Rob Campbell said a new push would be launched shortly.
By Rowan Quinn
