The traveller was infectious while on an international Jetstar flight from Thailand and a domestic Sydney-Melbourne flight with the same airline. They then boarded a Virgin Australia flight to New Zealand.

The traveller was on the following flights:

Jetstar JQ28 departing Phuket at 9:45pm on March 18, arriving Sydney Airport's T1 international terminal at 10:30am on March 19;

Jetstar JQ517 departing Sydney Airport's T2 domestic terminal at 2pm March 19, arriving at Melbourne Airport Terminal 4 at 3:35pm;

Virgin Australia Flight VA99 departing Melbourne Airport Terminal 2 at 6:35pm March 19, arriving at Christchurch Airport at 11:35pm.

People who were on the same flights or in Sydney Airport's international and domestic baggage carousels, customs, arrivals and departure areas between 10:30am - 2:30pm on March 19 are being urged to check for symptoms until April 6.

It can take up to 18 days for symptoms to develop after coming into contact with an infectious person.

NSW Health's Communicable Diseases Branch director Dr Vicky Sheppeard says people are susceptible to measles if they have never had the disease in the past or have not received two doses of the measles vaccine.

"The measles-mumps-rubella vaccine is free in NSW for anyone born during or after 1966 who hasn't already had two doses," Dr Sheppeard said. "If you're unsure whether you've had two doses, it's safe to have another."

Symptoms include fever, sore eyes and a cough followed three or four days later by a red, blotchy rash spreading from the head and neck to the rest of the body.

"If you develop symptoms, please call ahead to your GP to ensure you do not wait in the waiting room with other patients," Dr Sheppeard said.

Outbreaks of measles in popular tourist destinations, including countries in South-East Asia, means the risk for measles being imported into Australia remains high.

Measles is spread in the air through coughing or sneezing by someone who is unwell with the disease.