About 60 patients and 23 members of staff have reported symptoms of the gastrointestinal virus since Friday.
All are said to be recovering well from the illness, which is described as "mild but contagious".
One ward at Castle Hill Hospital in Cottingham has also stopped admitting any new patients.
Infection control
The Hull and East Yorkshire Hospitals NHS Trust said in a statement: "The virus, which is very common in the community, causes diarrhoea and vomiting for 24 to 48 hours.
"It is a mild but contagious illness that is spread by air and contact.
"All appropriate infection control procedures are in place and the hospital's infection control team is closely monitoring the situation.
"Non-urgent operations will be cancelled for the rest of the week."
Hospital staff who catch the bug are being advised to stay off work for at least 48 hours after their symptoms disappear.
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