It's understood a person infected with the condition took a flight from Dublin to the county in May and passed on the infection.
The Health Protection Surveillance centre says it's been notified of several cases in recent weeks in Dublin, Sligo, Mayo, Louth and Limerick.
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Measles is highly contagious and anyone with symptoms is being asked to contact their GP by phone and is urged not to travel to hospital or doctors' clinics.
