A person travelling from Phuket to Sydney,then on to Melbourne,and finally to Christchurch was diagnosed with the highly contagious disease.
Tourists who stayed at the Nomads All Nations Hostel in Melbourne last week might have been directly exposed to measles from another guest.
A person infected with measles visited inner Brisbane,West End and Brisbane Airport in the past fortnight,with a public health alert issued.
Two new cases of measles have prompted warnings for children at a school in the city's west and people in the CBD.
Health authorities have warned Sydneysiders and passengers on a Qantas flight from Bali to be on the lookout for measles symptoms.