Te Whatu Ora/Health NZ said the flights to Melbourne were Emirates flight EK408 from Dubai on 14 February and Singapore Airlines flight SQ217 from Singapore on 19 February.
Australian health authorities had told Health NZ that people in New Zealand were on those flights, along with confirmed measles cases.
"We are asking anyone who travelled on those flights to contact Healthline immediately and to stay home until they receive advice from public health services. Contacts may already be developing symptoms of measles so it is important to contact Healthline urgently," Health NZ said.
"If they do need to seek healthcare, they should phone ahead and wear a mask."
In 2019, a measles outbreak killed 83 people in Samoa. The vast majority of those were children.
Public health doctors have previously warned a measles outbreak was almost inevitable in New Zealand this year, because there were too many people not immunised.
Symptoms of measles include a fever, cough, runny nose, sore red eyes, and a rash beginning on the face and gradually spreading down the body to the arms and legs.
RNZ
