At least ten people are known to have caught measles in Dublin since the start of the year.
The HSE is treating it as an outbreak, and is working with the Health Protection Surveillance Centre to contain it.
Adults and children living and working around Parnell Street, Dame Street and Baggot Street have been affected.
It's understood someone who travelled back from France may have been infected first.
People who think they may have measles are advised to stay at home and contact their GP.
Measles is a serious illness and is highly infectious.
Symptoms include fever, red rash, red eyes, cough and runny nose.
You can find out more about measles on the Health Protection Surveillance Centre's website.
People who are sick should not attend settings such as crèche, school, work or religious gatherings until they have recovered from illness.