The face mask requirement has been in place since Wednesday, according to the Tribune de Genève newspaper.
It said the hospital, which was recognized for its flu-prevention strategy, was stepping up its efforts to protect patients against the virus this winter.
Only ten percent of visitors donned a mask last year.
From now on, anyone entering the building has to put on a mask – at the latest before going into a ward.
The hospital decided on the measure after identifying families and friends as the main reason for the spread of influenza among patients.
Until recently, the wearing of masks during flu season was highly recommended – but not obligatory – for visitors with a runny nose or slight fever.
The new rule means that even those visitors who are not suffering cold or flu symptoms have to cover their noses and mouths.
“If your nose is running or you have a fever, you should not even think of entering a hospital,” Didier Pittet, the hospital's head of infection prevention, told the paper.
“Wearing a protective mask is obligatory for everyone.”
Pittet said that while there were no concerns at present over the spread of the virus in the hospital, ten patients were currently infected.
Hospitals in the German-speaking part of the country have not yet followed the Geneva University Hospital's lead, 20 Minuten reported.
It quoted a spokeswoman for the University Hospital of Zurich as saying it was satisfied with visitors' response to the information it provided on preventing the spread of infection.
The University Hospital of Bern, or Inselspital, requires only that visitors displaying cold or flu symptoms cover their noses and mouths.
The Federal Office of Public Health says it will not make any recommendation to hospitals about imposing face mask rules.
People in Switzerland are less accepting of the idea than those in Asia, according to the head of the infectious diseases section, Daniel Koch.