Health chiefs are currently advising people to avoid six wards at the Queen’s Medical Centre and one ward at the City Hospital.
The wards in questions are F20, F18, B47, C51, C54 and B3 at Queen’s and Patience 1 at City.
A spokesperson for Nottingham University Hospitals NHS Trust, said: “Purely as a precautionary measure we ask relatives and friends only to visit affected wards if it is absolutely necessary.
“This helps us to reduce the spread of the virus and minimise the risk to visitors who may become ill or take the virus back into the community.
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“It also helps us to clear the infection from the war as quickly as possible.”
They are also asking people who have had the bug not to visit the hospital for 72 hours after their symptoms have disappeared.
The most common symptoms of the virus are nausea, vomiting and diarrhoea, but some people may also have a raised temperature, headaches and aching limbs.
Symptoms usually begin around 12 to 48 hours after becoming infected and will usually last for 12 to 60 hours.
Most people make a full recovery within a couple of days, however vulnerable people may become very dehydrated and require hospital treatment.
If you are worried about yourself or a family member, call your GP or the NHS on 111, but try to avoid going to your GP as this will help stop the bug spreading.