NHS Greater Glasgow and Clyde chiefs say those who have experienced flu symptoms in the last 48 hours should not visit patients who are already unwell.
They also said hospitals including Queen Elizabeth University Hospital, Gartnavel General and Glasgow Royal Infirmary are experiencing “unusual winter pressures”.
Dr Emilia Crighton, deputy director of public health said: “Influenza is more than a bad cold and even young healthy people can feel unwell with flu for a week or more.
“We would urge anyone who has experienced any flu symptoms within the last forty-eight hours not to visit hospital as it could be passed on to patients who are already very unwell.
“If you are well enough to visit, please remember to keep your hands clean by washing and using antibacterial gel. Clean hands are the best way to stop spreading infection.”
In a statement health bosses said they have a range of out of hours support for patients, including pharmacies, GP Out of Hours services, which are fully staffed and operational.
Minor Injuries Units (MIUs) will be extended with the addition of the West Glasgow MIU which opens on January 3.
A spokeswoman added: “Our hospitals are experiencing the usual winter pressures.
“Therefore we are urging patients to attend the most appropriate service for their healthcare needs.”