All internet users are being warned to avoid clicking links or attachments on unknown emails.
Digital security experts say the so-called "Wannacry" ransomware can infect whole networks with just one click.
The virus targets files and demands payment in order to unlock them. It has already affected more than 70 countries worldwide.
The Government says the National Cyber Security Centre is in close contact with the Gardaí and HSE on the issue.
The HSE has taken precautionary measures to protect its IT network after the UK's health service was hit. The virus means doctors are unable to access online patient records. Some hospitals were forced to cancel and delay operations after computer systems were crippled.
Europol says the attack is on an "unprecedented" level and added that it'll require a "complex international investigation to identify the culprits".