Yesterday a further 71 cases were identified in England.
A second case of monkeypox has been confirmed in Ireland.
It comes as 179 cases have been confirmed across the UK.
In a statement last night, the HSE said Public Health is carrying out contact tracing for both cases identified here, and is following up with anyone who had close contact with the case while they were infectious.
Public health risk assessments have also been carried out, and those who were in contact with the cases are being advised on what to do in the event that they become ill.
The first case of monkeypox was confirmed in Ireland last Friday night in the east of the country.
The HSE says the cases here were not unexpected, considering the presence of the virus in the UK and many European countries.
Yesterday a further 71 cases were identified in England - bringing the confirmed UK total to 179.
People there are being advised to stop having sex and to use a condom for eight weeks after an infection.
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