The affected wards are E3, C2, G1 and G3.
The hospital said restrictions would not apply to paediatric, maternity or end-of-life patients.
Norovirus is the most common cause of infectious diarrhoea and vomiting in England and Wales, according to the NHS.
It can be transmitted by contact with contaminated surfaces and objects, and people usually recover fully within two to three days.
The hospital said: “Please do not visit someone in the hospital if you are experiencing symptoms of norovirus – wait until you have been symptom free for at least 48 hours.”