NHS Greater Glasgow and Clyde said that 13 patients were showing symptoms of norovirus at the city's Victoria Infirmary.
All three of the wards affected at the South Side hospital are medical wards.
Dr Pauline Wright, infection control doctor, NHS Greater Glasgow and Clyde, said: "Norovirus is particularly prevalent during the winter and it is not unusual to see this type of virus in the community and also in healthcare settings.
"All appropriate infection control measures are in place and we are also urging any visitors who have experienced diarrhoea or vomiting within the last 48 hours not to visit the hospital."
Dr Wright reminded visitors of the importance of hand hygiene when entering and leaving hospital premises.
She added: "This virus is extremely common in the wider community and therefore we would like to remind hospital visitors of the importance of hand hygiene when entering and leaving hospital premises.
"Alcohol gel hand wash is available throughout the hospital at the entrance and exits of wards and at each patient bed space."