The Department of Health (DoH) has issued a warning for any one who was at Royal Perth Hospital (RPH) on July 3 and 6 or at Bentley Hospital on July 2 and 5.
A person who was at RPH and Bentley Hospital on these days has been confirmed to have measles.
If not immune, exposed people who attended the hospitals on these days could develop symptoms of the disease from now until around July 24.
An unimmunised traveller who was infected while holidaying overseas attended the Emergency Department at RPH on June 21 and 24 and has been identified as the original source of the infection.
That person also spread measles to two family members and another patient attending the Emergency Department at that time.
Contact associated with the most recent case is believed to be limited, but the necessary precautions are being taken by advising known contacts, including both staff and patients.
According to DoH, measles is highly infectious to non-immune persons and is spread by airborne respiratory droplets.
The incubation period is usually 10-14 days but may be up to 18 days.
Clinical illness from measles usually begins as fever, cough, runny nose and sneezing and conjunctivitis (red, sore eyes), before the characteristic blotchy red rash appears after about three to four days.
Measles is infectious up to five days before the rash appears, and usually for about 4 days after appearance of the rash and can be a serious illness, especially in young children and other vulnerable people.
Around 50 per cent of cases may require hospitalisation, and complications include pneumonia and encephalitis.
People who have not been vaccinated against measles or have received only one dose of vaccine may still be susceptible to infection.
About 99 percent of people who receive the recommended course of two vaccinations will be immune to measles.
People born before 1966 have a high probability of being immune through prior natural infection.
A family of five unimmunised children also recently acquired measles from an unknown source in WA.
These incidents are a reminder of the importance for all Western Australians to be fully vaccinated against measles and other infectious diseases, including when travelling overseas.
The DoH is warning anyone who thinks they may have measles to stay at home and not go to public places.
If they need to attend a GP or hospital they should phone ahead so that precautions can be taken to ensure they do not sit in waiting rooms and clinical areas where they may infect other patients and staff.
For more information go to public.health.wa.gov.au
