Fourteen patients and a number of staff members at St Vincent's University Hospital in Dublin have been hit by the so-called winter vomiting virus.
The hospital today asked the public to only visit patients at the hospital if absolutely necessary. It also asked that people attend the emergency department only if necessary to help curtain the spread of the illness.
Children should not be brought to visit patients at the hospital, a statement said.
"These visiting restrictions are essential for the health and safety of patients, visitors and staff."
Symptoms of the virus include nausea, vomiting and watery diarrhoea. Although most people recover within one to two days, some people, usually the very young or elderly, may become very dehydrated and require hospital treatment.
The virus is easily spread from person to person and can survive in the environment for days, making it difficult for hospitals to contain.
People infected are contagious from the moment they begin feeling ill until two to three days after recovery. Some people may be contagious for as long as two weeks after recovery.