The attack has hit 200,000 victims in at least 150 countries
The HSE have issued a warning for all its staff members after a global cyber attack affected institutions around the world.
They said "Following the attacks on the NHS on Friday which limited the delivery of many of services in the UK, the HSE has been working over the weekend in order to prevent its Network from being compromised.
"As staff go back to work tomorrow, the HSE is advising all of its staff to TURN ON their computers but DO NOT LOG ON for a full two hours.
"This will allow the anti-virus capability to become active while still allowing the Network will remain protected.
"Each health building will have an IT representative to provide assistance in the morning.
"There is also a dedicated help-desk function in place for dealing with this crisis. An important message for all computer users is THINK BEFORE YOU CLICK."
The head of the EU security agency Europol says a ransomware cyber attack has hit 200,000 victims in at least 150 countries.
Director Rob Wainwright told ITV: "At the moment, we are in the face of an escalating threat. The numbers are going up. I am worried about how the numbers will continue to grow when people go to work and turn on their machines on Monday morning.
"The global reach is unprecedented. The latest count is over 200,000 victims in at least 150 countries, and those victims, many of those will be businesses, including large corporations."
Mr Wainwright said the attack was indiscriminate, fast-spreading and unique because the ransomware was being used in combination with a worm which means the infection of one computer could automatically spread it through a whole network.
Few banks in Europe were affected after learning from previous experiences of attacks, Mr Wainwright said but an attack on public health systems, which badly affected the NHS in Britain, had caused concern.
He said: "We have been concerned for some time that the healthcare sectors in many countries are particularly vulnerable. They're processing a lot of sensitive data."
Mr Wainwright said Europol was working with the FBI to track down those responsible and said it was likely more than one person was behind the attack but he said identifying offenders was "very difficult".
"We're in a very difficult fight against these ever more sophisticated cyber crime syndicates that are using encryption to hide their activity," he said.
It is feared more cases of the 'Wannacry' cyber attack will be uncovered in Ireland as businesses re-open tomorrow.
A small Health Service Executive (HSE) funded healthcare facility in Wexford was among thousands across the globe affected by the ransomware.
However it is not connected to the health authority's network.
The HSE is working to secure thousands of its devices, having taken steps to reduce the risk of disruption - including removing access for incoming communications.
The National Cyber Security Centre (NCSC) says it continues to actively monitor the situation, and engage with Government and the private sector.
In a statement, the NCSC said: "The situation is still evolving, but international contacts are ongoing and more clarity is becoming available on an hourly basis as to how this malware propagates and how it can be dealt with."
The NCSC also said the affected centre in Wexford does not pose "a broader risk".
"Efforts will continue over the weekend and into next week to ensure that services across the public sector remain unaffected and that the private sector receives any support or information required", the NCSC added.
Business group IBEC is advising members to take extra vigilance regarding cyber security.
Its head of digital policy, Erik O'Donovan, says: "Safeguarding the resilience of our digital infrastructure and economy is a key priority for business.
Ibec has previously called for adequate resourcing of the National Cyber Security Centre and the implementation of a cyber security programme.
"Government provided extra funding in this regard to the Department of Communications, Climate Action and Environment in Budget 2017 and in view of the increased threat we call for this funding to be increased significantly further.
"Adequate cyber security infrastructure is of critical importance to all companies in Ireland and is a major consideration in securing inward investment.
"The business sector invests heavily in cyber security and it is essential that the Department of Communications, Climate Action and Environment has adequate resources to address the related policy issues including the implementation of the Directive on Security of Network and Information Systems."
Russia appeared to be the hardest hit nation, with its interior and emergencies ministries and biggest bank, Sberbank, saying they were targeted.
The interior ministry said on its website around 1,000 computers had been infected but it had localised the virus.
Tech journalist Andy O'Donoghue says the scale of the situation is unprecedented.
"I think the scale of this outbreak is what's worrying.
"Generally when we see ransomware attacks we see them, they occur to individuals (and) to small businesses.
"But this is a ransomware attack that appears to have affected 100 countries and tens of thousands of individuals.
"So this is a really, really serious attack".
Ransomeware is the term applied to a type of malicious software (or 'malware') that infects a victim computer and encrypts the hard drive, rendering the information on it unreadable.
The malware then instructs the victim to pay a sum of money to an account, at which point a code will be issued which decrypts the hard drive.
Additional reporting: Aisling O'Rourke/IRN