Public health nurses had spent the week trying to trace everyone from flight SQ281, which arrived from Singapore last Sunday.
Hoskins said 216 passengers were living or staying in Auckland, according to information supplied by the airline.
The remaining 50 passengers lived elsewhere in the North Island and Southland and Otago.
"We have traced most of those on board but are having difficulty getting in touch with people who did not leave a valid phone number or email address on their passenger arrival card," said a spokesperson.
No new cases had come to light in recent days, although health officials said it was early in the incubation period, which ranged from eight to 21 days.
People contacted were given advice, including the need for isolation and further immunisation.
Passengers born after 1969 were of chief concern to public health workers as they may not have been immunised. Travellers older than 45 were considered less at risk as they were likely to have been exposed to the disease and have acquired immunity.
Hoskins said people who felt unwell should phone their doctor or Healthline on 0800 611 116 for advice.
Singapore Airlines' New Zealand general manager Edwin Chiang said the company was contacted by authorities on Tuesday about the measles scare and had assisted New Zealand and Singapore health officers with customer contact information.
None of the 11 cabin crew had reported any symptoms but had been advised to monitor their health closely.