The HSE is appealing to the public to help stop the spread of the winter vomiting bug.
Three hundred cases have been reported in recent weeks, and hospitals, nursing homes and hotels are affected.
Fifty cases in a normal week would be considered high but that can rise to between 1,000 and 5,000 during busy periods.
The HSE's Health Protection Surveillance Centre has asked visitors to respect restrictions at hospitals and to follow hand hygiene directions when they are visiting.
Norovirus is highly infectious and spreads through contact, the air, and via surfaces.