Restrictions have been placed on four additional wards at Hairmyres Hospital in East Kilbride, South Lanarkshire, with no new patients being admitted to certain areas of them.
NHS Lanarkshire said that 63 patients and 28 staff have experienced symptoms of the bug since the outbreak began about a week ago.
Eight patients and three staff remain symptomatic.
The health board said that strict standard infection control precautions are in place under the guidance of infection control specialists.
The situation is being monitored on a daily basis and the hospital remains open to emergency admissions as normal.
Susan Friel, chief of nursing services at Hairmyres Hospital, said: "Our priority is always to ensure the safety of our patients and our clinical staff are trained to deal with such situations.
"We have a comprehensive range of infection control measures in place to manage the risk of the infection.
"No new patients are being admitted to wards that have been affected until our infection prevention and control team are satisfied these restrictions can be removed."
She added: "It is important that people do not visit hospital if they feel unwell or are themselves experiencing symptoms of diarrhoea and/or vomiting, as this increases the risk of spreading the infection to patients and staff.
"People who feel unwell or think they have the symptoms of norovirus should wait until they have been clear of them for at least 48 hours as they may still be infectious.
"Patients and visitors can also help us to control the infection by maintaining good hygiene, especially regular hand-washing with soap and water before visiting and when leaving the ward area, before eating and after visiting the toilet."
As part of the infection control precautions, flexible visiting times have been temporarily suspended, with current visiting hours for all wards from 3pm to 4pm and 7pm to 8pm.
Members of the public are also being reminded to respect normal visiting rules which advise that a patient can have two visitors at a time on the ward and that children should not be brought into wards.
Norovirus is the most common stomach bug in the UK, affecting between 600,000 and one million people of all ages every year.