The virus, which causes diarrhoea and vomiting, has been confirmed on Fairoak ward and visiting times are being restricted to an hour while the outbreak is managed.
Visitors are asked to only visit the ward between 1.30pm and 2.30pm – with only two visitors per patient.
People planning on visiting the hospital are being asked to stay away if they have experienced any of the symptoms of norovirus, or have been in contact with anyone who has norovirus in the last 72 hours.
Sometimes known as the winter vomiting bug, it is the most common stomach bug in the UK.
It is highly contagious and can affect people of all ages.
Matt Reid, head of infection prevention at The Royal Wolverhampton Trust which runs the hospital, said: "We have had an outbreak of norovirus on Fairoak.
“Visiting times to this ward will be restricted to an hour.
“Please call the ward before visiting and do not visit hospitals or care homes if you, or the people you live with, have had diarrhoea, vomiting or flu-like symptoms in the last 72 hours.
"If you are unsure whether to visit, please feel free to contact the ward nurse before you come into hospital."
He added that good hand hygiene can help limit the spread of the infection.
Matt said: “Wash your hands frequently and thoroughly with soap and warm water, particularly after using the toilet, and before preparing food or eating.”
The norovirus symptoms include suddenly starting to feel sick, experiencing projectile vomiting, having watery diarrhoea, and experiencing a slightly high fever, headache, painful stomach cramps and aching limbs.