The Ministry of Health is warning people who arrived in New Zealand on an Emirates flight from Dubai via Australia on Tuesday, 4 January to check themselves for measles symptoms.
One passenger, who disembarked in Melbourne, has been confirmed as having the viral disease.
The Health Ministry says measles is easily spread through the air and people sitting in a row close to the affected passenger could be at risk.
The Ministry's chief advisor on population health, Dr John Holmes, says there were about 20 people within close proximity whose whereabouts in this country are unknown.
Dr Holmes says people tend to underestimate measles but the reality is one in 10 people who contract it need to be hospitilised.
If people on flight EK406 have developed a fever or rash they should call Healthline on 0800 611 116 rather than going to hospital, where they could infect others.