The case transited through Melbourne Airport’s T2 international terminal between Wednesday, February 14 at 10.50pm and 12.20am on Thursday, February 15.
The case also went through the T1 domestic terminal on the Thursday between 1.30pm and 2.35pm before travelling to South Australia.
People who were at Melbourne Airport during these times should monitor for symptoms.
The case subsequently visited several locations in Adelaide.
The South Australian Government has issued a list of exposure sites.
Anyone who has returned to Victoria from South Australia, and attended one of the South Australia exposure sites, should monitor for symptoms for 18 days after their exposure.
Measles is a highly infectious viral illness that spreads easily among those who are not fully vaccinated.
Young children and adults with weakened immune systems are the most at risk of serious illness.
People who attended the exposure sites are urged to seek medical care if they develop symptoms, and to wear a mask and call ahead to ensure they can be isolated from others.
The illness usually begins with fever, runny nose, cough and conjunctivitis, followed by a rash.
The characteristic maculopapular rash usually begins three to four days after the first symptoms, generally starting on the face and then spreading to the rest of the body.
“People who were at any of the exposure sites should monitor for symptoms and seek medical attention if they become unwell,” Victorian chief health officer Clare Looker said.
Recent Victorian cases of measles have been identified in people who were not fully immunised against measles and who had travelled overseas or been in contact with returned overseas travellers.
Measles is rare in Australia because vaccination is effective in preventing the disease.
“People who are planning to travel overseas should ensure they have received appropriate vaccinations, including the measles-mumps-rubella vaccine if they don’t have a history of two previous MMR vaccinations,” Dr Looker said.