A suspected case of the ransomware that is sweeping the world has been identified in a computer system in a healthcare facility in the south-east of the country.
The infection at the centre in Wexford has been isolated and prevented from spreading.
The voluntary organisation is partly funded by the Health Service Executive under Section 39 of the Health Act 2004, but is not controlled by the Government agency and is therefore not part of its IT network.
However, IT specialists in the HSE are providing support to the organisation to help it to deal with the issue and are confident the malware has not spread into its systems.
Earlier, the HSE said it will take a number of days to secure 1,500 devices on its networks that are considered vulnerable in light of yesterday's global cyber threat.
The HSE yesterday said it was taking precautionary action to protect its IT systems following a major ransomware attack on the NHS.
The Taoiseach has said the global cyber attack issue is a very serious matter and is being monitored very closely.
Speaking in Sligo this morning, Enda Kenny said the situation was being monitored on an hourly basis.
As a precautionary measure yesterday, the HSE cut its networks off from external traffic and declared it a major incident.
In an update this afternoon, the HSE said: "There are approximately 1,500 devices that are considered either threatened or targeted devices. This includes devices that deliver diagnostic imaging (NIMIS) and Bio-Medical Device control machines."
Anti-virus updates are being installed in these devices, but it is expected this process and testing will take a number of days.
It said all health services staff are advised to have an increased level of digital vigilance while this cyber threat exists.
Yesterday's massive and rapid cyber attack has seen large numbers of computers in around 100 countries locked by the virus, which demands payment of a ransom for the files to be released.
A form of so-called ransomware, the WannaCry virus is based on hacking tools thought to have been developed by the US National Security Agency.
The tools were stolen from the NSA by a group called The Shadow Brokers, which then released them onto the internet.
And although Microsoft issued a security patch for the vulnerabilities in March, it seems hackers have now used the tools to attack computers that have not been fixed since or are too old to be protected.
Among the estimated 75,000 cases recorded globally so far are systems of NHS hospitals in Britain, Spanish and Portuguese telecoms firms, and the delivery company FedEx.
The Minister for Communications has acknowledged there could be a big problem for the HSE and its patients if the threat of the ongoing cyber attack has not receded by Monday.
Denis Naughten said the threat is being faced by not only the HSE and the likelihood is that next week attacks may be recorded here because there is a lot of legacy equipment in both the public and private sectors.
He said he has received a full briefing from the team in the National Cyber Security Centre (NCSC), which is monitoring the situation.
The Government is working closely with European counterparts and An Garda Síochána, he said, and Mr Naughten said he has spoken to the Tánaiste and Minister for Health this morning.
Speaking in Dublin, Mr Naughten said the fact there has not been a successful attack so far in Ireland is down to luck in some instances but also proactive work by agencies including the HSE.
He said there is no need for patients to be concerned and people should be proud of the fact the HSE seems to have been ahead of the curve regarding the issue.
The minister said a number of things have to be done to guard against the threat, including raising awareness and encouraging people to use the patches made available by the technology companies.
Asked if the Government would be raising concerns with the US government over the reported links between the malware and the US National Security Agency, Mr Naughten said there is a lot of speculation out there about who is behind this, but he is not going to comment on that until there is evidence.
He said the general threat of cyber attacks is an ongoing issue for the Government.
Europol has said the wave of cyber attacks wreaking havoc across the globe is "at an unprecedented level".
In a statement, it said the attacks will "require a complex international investigation to identify the culprits".
Companies advised not to pay ransom
Meanwhile, the head of PWC's cyber security threat intelligence and IT forensics team has said his advice to companies hit by yesterday's ransomware hack is not to pay.
Pat Moran acknowledged "the threat to remove files is very real" but said "our guidance would be not to pay".
Mr Moran said what was different about yesterday's attack was the scale and sheer speed of the attack.
He said after the NSA was hacked six weeks ago and had hacking software stolen, "it was inevitable that an attack like this was going to happen".
Organisations have been urged to update patches to their systems.
Mr Moran said the hack is usually sent via a phishing email with an attachment. PWC is advising its clients to be aware of suspicious emails and report those types of emails.