NHS Lothian has confirmed that since the winter vomiting bug outbreak started on January 29, 51 of the 151 patients at Liberton Hospital, Edinburgh have been struck down.
Seventeen members of staff have also contracted the bug.
Eight of the nine wards are currently closed to new patients as part of strict infection and prevention control procedures.
It follows warnings by the Government of high levels of flu and norovirus, and reports of chaos in Scottish hospitals. Patients have had to wait on trolleys for hours because of the high number of admissions and the shortage of available beds.
NHS Lothian says relatives and friends of patients are now being contacted by staff and are being advised not to visit the hospital, which provides acute, rehabilitation and ongoing care for older people.
The board said: "The situation is being continually monitored and relatives are asked to contact the hospital if they require any further information."
The development comes after it emerged earlier this month that 53 people have been admitted into intensive care with flu this winter season, and the virus has so far claimed 11 lives.
The majority of those deaths and illnesses have come this year, prompting concerns the weather could be to blame.
Dr Ingolfur Johannessen, chairman of the incident management team and consultant medical virologist at NHS Lothian, said: "A large number of patients at Liberton Hospital are affected by norovirus, with a significant number testing positive for the virus.
"We have taken the decision to temporarily restrict visitors in a bid to prevent the further spread of the infection and to ensure the hospital returns to normal working as soon as possible.
"By restricting the number of visitors it is hoped that this will reduce the number of people who are exposed to norovirus and therefore shorten the duration of the outbreak."
Professor Alison McCallum, director of public health and health policy at NHS Lothian, added: "Our priority is always patient, public and staff safety.
"While we understand this temporary visiting restriction may cause some frustration, this measure will allow us to help prevent further spread of the infection and ensure safe patient care.
"We understand there may be extenuating circumstances where members of the public need to visit loved ones, such as if they are seriously ill. If this is the case, relatives or friends are asked to call ahead to the ward to arrange visiting."
The health board said infection prevention and control staff were continually monitoring the situation and it was hoped the hospital would reopen to visitors in the very near future.
Figures recorded by Health Protection Scotland show a drastic rise in flu cases this winter compared to 2011/12, when only 17 people were admitted to intensive care and five died. However, recorded cases for 2010/11 were far higher, with 177 intensive care admissions and 63 deaths.
This winter, eight children and 21 patients aged 65 and over have been taken into intensive care with flu. The ages of the 11 people who have died have not been released.
The latest figures show appointments with family doctors about flu symptoms have risen again, to 44 per 100,000 of the population in the fourth week of the year, which ended on January 27. The rise came after hopes the rate had peaked in week two of 2013 (52 per 100,000), given a decrease in week three.
Norovirus symptoms include vomiting, diarrhoea and nausea, which come on suddenly and last between 12 and 60 hours.
The advice to those who catch norovirus is to drink plenty of non-alcoholic, non-milky liquids to replace lost fluids.