The infection was reported in the east of the country on Friday night and the person affected was not kept in hospital.
A further suspected case is also being investigated and test results are being awaited, health officials said.
A statement from HSE said: “The Health Protection Surveillance Centre was notified last night of a confirmed case of monkeypox in Ireland, in the east of the country.
“This person has not been hospitalised.
“This was not unexpected following the presence of monkeypox cases in the UK and many European countries.
“Public Health is following up those who had close contact with the person with monkeypox while they were infectious. In order to maintain patient confidentiality, no further information about this person will be provided.
“A suspected case is also being investigated and test results are awaited.
“A public health risk assessment has been undertaken and those who were in contact with the person are being advised on what to do in the event that they become ill.”
Monkeypox causes unsightly blisters - the ‘pox’ - referred to as ‘lesions’ by doctors. In most people it is a mild illness that clears up after a few weeks. Other typical symptoms include fever, aches and fatigue.
However, it can cause serious complications including brain swelling, sepsis and vision loss.
West African outbreaks have reported a fatality rate of about one per cent.
So far there have been 106 cases confirmed in the UK.
The UKHSA previously said “a notable proportion of early cases detected have been in gay and bisexual men” or men who have sex with men so it was “urging this community in particular to be alert”.
A similar pattern of infection has been seen in Italy, Spain and Portugal and several of those infected had attended the Maspalomas Pride festival on Gran Canaria this month.