The woman (who was unaware she had the highly-contagious disease) had been in Geelong, central Melbourne and the bayside suburbs during the incubation period.

While infectious, she stayed in Shepparton from June 21 to 25, before travelling by train to Southern Cross Station on Saturday June 25 and then on to Melbourne Airport the same day.

Queensland health authorities have also issued an alert after the woman flew on Jetstar flight JQ574, which departed Melbourne about 10.30am. She stayed in Brisbane for three days.

Authorities are contacting people who may have been in close contact with the woman.

However, Victoria's acting Chief Health Officer warned that others may have unwittingly come into contact with the virus, as it can live for up to two hours in an airspace where the infected person has coughed or sneezed.

Dr Finn Romanes warned the public to be alert to symptoms- including fever, sore throat, red eyes and coughing.

"Measles has an incubation period of up to 18 days, so illness acquired from contact could still be coming through," he said. "Subsequent cases could still remain infectious for many days."

Measles is rare in Victoria because of widespread use of the measles vaccine and most cases are linked to international travel, with the disease more prevalent overseas.

Dr Romanes said the woman in this instance had not been overseas, so it was likely they had become infected through contact with someone who had travelled overseas.

Measles is a highly-infectious virus that can cause serious illness. Patients can develop pneumonia and other serious complications from the disease, and those with measles often need to be hospitalised.

The viral disease lives in the nose and throat mucus of an infected person and sufferers can spread the virus for several days before symptoms begin to show.

The characteristic measles rash usually appears three to five days after the first symptoms develop, generally starting on the face and then spreading to the rest of the body.

"Anyone developing these symptoms should ring ahead to their doctor or hospital and alert them that they have fever and a rash which may indicate measles," he said.

"The doctor or hospital will then be able to provide treatment in a way that minimises transmission to others."

Children who have had both courses of the vaccine are extremely unlikely to be at risk.

There have been 32 measles cases in Victoria so far this year, compared with 27 cases for the same period last year, according to the Health Department.

Latest figures show that 94 per cent per cent of Victorian children aged up to five years are fully immunised against measles.