Four wards have been closed because of patients experiencing viral diarrhoea and vomiting.
To prevent the virus spreading, the hospital, in Pield Heath Road, has also implemented temporary visiting restrictions.
In a statement, Hillingdon Hospitals NHS Foundation Trust, which runs the hospital, said: “This is a difficult decision to make, as we are aware of the effect restricted visiting may have on patients and their families. However, our priority has to be the protection and safety of our patients.
“The situation is reviewed on a daily basis and follows current guidance on managing norovirus within healthcare settings.”
Norovirus is extremely infectious and causes diarrhoea and/or vomiting.
The trust said the virus could “spread rapidly through our patients and staff, causing significant disruption to the day to day running of the hospital”.
The trust has issued the following advice for affected members of the public:
Wash and dry your hands thoroughly after going to the toilet and before you handle food
Drink plenty of water to avoid dehydration and return home and let the illness run its course
Do not visit your GP surgery or local A&E unit. Norovirus infection is a self-limiting illness and you will recover naturally without treatment
Do not visit friends or relatives in hospital or residential care homes, as there is a real risk you will introduce the infection into the establishment
People with diarrhoea and vomiting should seek medical advice if their symptoms last for more than 48 hours, or if they have a pre-existing medical condition. If patients have concerns they should call their GP or 111
Stay away from work or school until you have been free of symptoms for at least 48 hours
The elderly and the very young can sometimes get more severe infection or become dehydrated. If that should be the case, they or their family, friends or carers should telephone their GP service, or NHS Direct, for advice
Do not handle or prepare food for other people until you have been symptom-free for a minimum period of 48 hours