"We are asking that anybody who is visiting patients at Middlemore Hospital be well and show no symptoms of illness and have been symptom-free for at least two days," said a hospital spokeswoman.
"No children will be allowed into wards unless it is on compassionate grounds, and Ward 5 has a requirement that visitors [put on] gowns and gloves before visiting affected patients."
Norovirus is often transmitted by eating uncooked shellfish, but it can also be transmitted through airborne particles and contaminated surfaces, such as door knobs.
Hospital visitors and people in the community are encouraged to wash their hands thoroughly to help stop the spread of infection.
There is no specific treatment against the virus, which usually stays in the body for between 12 hours and three days, though extra fluids and rest are recommended.
People with symptoms are urged to avoid contact with infants, the elderly or those with long-term illnesses.
