A further suspected case is also being investigated
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 public health risk assessment has been undertaken and those who have been in contact with the person are being advised on what to do in the event that they become ill.
Monkeypox is a viral infection that has a a six-to-16 day incubation period and sees patients first suffer fever, headaches, swellings, back pain, aching muscles and a general listlessness in its opening stages.
Once that passes and the fever breaks, the sufferer will experience a skin eruption, in which a rash spreads across the face, followed by the rest of the body, most commonly the palms of the hands and soles of the feet.
The blemishes evolve from lesions into crusted blisters, which can then take three weeks to heal and disappear.
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 was not unexpected following the presence of monkeypox cases in the UK and many European countries,” it added.
“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.”
The UK Health Security Agency (UKHSA) said the new cases bring the England total since May 7 to 101, and the UK total to 106.
There have been three confirmed cases in Scotland, one in Wales and one in Northern Ireland.
The first cases of monkeypox in Wales and Northern Ireland were recorded on Thursday while Scotland confirmed a further two cases.
Almost 200 cases have been reported in more than 20 countries not usually known to have outbreaks of the virus, according to the World Health Organisation.
Follow the latest on monkeypox news here.