Update 3.10pm: The HSE is rebooting more than 1,200 servers this afternoon in order to activate additional security updates designed to address the WannaCry ransomware virus.
The planned IT outage is underway across the network.
The executive says any significant disruption to patient services is not anticipated and business continuity processes are in place to protect the delivery of patient care.
The HSE says there have been no reports today of any additional suspected cases of the ransomware attack and the executive is continuing to monitor the situation.
Update 9.10am: The Cabinet will be briefed on the fallout from the global cyber virus attack later.
The HSE's external IT networks will also remain offline today as a precaution.
The only confirmed case in Ireland so far is a HSE-funded healthcare unit in County Wexford - which was not connected to its main network.
Communications Minister Denis Naughten will speak to Ministers later.
“We have been lucky in that we have been upgrading our computers and hardware, particularly in the last few years.
“We have ramped up resources right across government to IT support and as a consequence have been quite lucky that we haven’t had a successful attack on than this one.”
Two cyber security firms have suggested a North Korea-linked organisation is behind the attack that's crippled compuer systems around the world.
Lazarus Group is thought to have targeted Sony Pictures in 2014.
Earlier: Workers across the Republic of Ireland and the North have been placed on high alert over cyber security.
Family doctors in Ireland have been warned not to use their practice computers until they are certain their anti-virus security systems are up to date after a mass hack which has spread around the world since Friday.
The PSNI said some people's systems may already be infecting and waiting to activate after the weekend.
More than 200,000 computer systems in nearly 100 countries have been infected with the so-called WannaCry ransomware since Friday.
The software locks files or a whole machine until a ransom is paid.
The malware has caused severe disruption to health services, industry, transport, academia and law enforcement around the world.
The Health Service Executive (HSE) cut its network off from external communications as a precaution.
The decision means its facilities will be unable to receive emails from outside the organisation.
But HSE chief information officer Richard Corbridge said the impact on patients is unlikely to be significant because email is rarely used to communicate with patients.
Detective Chief Inspector Douglas Grant, head of PSNI Cyber Crime Centre, said: "While no incidents have been reported in Northern Ireland as yet, we do expect further infections to come to light globally over the next week and we cannot rule out the possibility that local systems may be vulnerable.
"As people return to work tomorrow after the weekend, many will have unopened, potentially infected emails in their inboxes, or their systems may already be infected and are waiting to activate.
"It is of the utmost importance that individuals and organisations act to ensure the integrity of our local cyber networks and take appropriate action to reduce the threat posed by cyber criminals."