It said it had taken the precaution of closing down its systems to further protect them, and to allow it to assess the situation.
Irish broadcaster RTÉ said Dublin's Rotunda Hospital has cancelled most outpatients visits on Friday.
All gynaecology clinics are cancelled.
However, it said those with any urgent concerns should attend as normal.
The maternity hospital says all outpatient visits are cancelled, unless expectant mothers are at 36 weeks pregnant or later.
The HSE has apologised to patients and the public and said it would give further information as it becomes available.
Computer viruses that threaten to delete your files unless you pay a ransom are known as ransomware.
Like other computer viruses, it usually finds its way onto a device by exploiting a security hole in vulnerable software or by tricking somebody into installing it.