Minister for Communications Eamon Ryan has said a cyber attack on the Department of Health "wasn't as extensive" as the similar ransomware attack on the Health Service Executive.
Minister Ryan said the attack on the Department was "intercepted earlier" and there is "no sense of any other agencies being affected" at this stage.
"I am confident that their systems will probably be back sooner," he said.
"This is very commonplace unfortunately ... our systems are always under attack," he added.
The Department of Health has also shut down its systems and it is working to safely restore its data.
In a statement the Department confirmed that late last week it was subject to a ransomware attack and have been working to respond to the incident since Thursday.
"We continue to assess the impact across all our systems and our focus is on protecting our data," the statement said.
RTÉ News has learned that a digital note from the cyber crime group believed to be responsible has been left on the Department's IT systems, similar to the one discovered at the HSE
The National Cyber Security Centre, along with the gardaí and the Defence Forces, are investigating the attacks.
They are also working with Europol and believe the attack is criminal, not espionage.
Digital footprints of the malware inserted by the criminal group into the Department and the HSE systems are being sent to the Europol Malware Analysis System in the Hague.
These will be analysed to determine the nature of the computer virus and if it has been used anywhere else before.
The attack on the Department of Health is believed to be similar to the attack on the HSE's systems.
Investigators suspect both ransomware attacks have been committed by the same organised cyber crime group, which they believe is eastern European.
The HSE said this morning it is unaware of any of the detail of any ransom request for the restoration of its systems.
It confirmed a message was left on its systems confirming the ransomware attack with a link to click for more information which would lead into a chat on the darknet.
The HSE said it did not engage but passed the information on the National Cyber Security Centre which is the lead response agency in cyber attacks on critical national infrastructure.
Meanwhile, the Department of Social Protection has temporarily suspended a number of electronic communication channels with the HSE while the health service's systems are offline.
The Department of Social Protection says its systems are fully operational and are monitored at all times
It said it has cyber defence systems in place which react to any threat to its systems in the event of a cyber incident.
Additional reporting Aengus Cox