There have been more than 30 cases of the potentially deadly virus this year, despite the disease having been eradicated from Australia.
Metro North Public Health Unit director Dr Susan Vlack says the patient was diagnosed on November 30, but authorities haven't identified the source of the infection.
She says the patient visited Chermside, Deception Bay and Redcliffe while infectious and people living in those areas should be alert to symptoms.
"Because the patient has no link to an identified case, there are likely to be other cases in the community," Dr Vlack said in a statement.
"If you are unwell with symptoms of measles, you should contact your GP to make an appointment.
"You should inform the practice that you may have measles, so that other patients can be protected from exposure."
Measles symptoms include fever, cough, runny nose, then a red spotty rash and sore eyes a few days later.