Mr de Wet said it was a 24-hour bug. It typically lasted one to two days and settled down without treatment.
For the most part, norovirus was a mild to moderate condition but could make recovery more difficult for those already in hospital, he said.
"If someone does have other conditions it could be more serious."
Mr de Wet said those with the virus had been grouped together to restrict the spread of the virus and the hospital had made one general medical ward available for use.
"Ideally patients are isolated or grouped together with patients who also have the virus."
There are controls and restrictions on movement throughout the hospital, although visitors are still allowed. "Visiting is allowed although we are trying to avoid unnecessary visiting or particularly large groups visiting," Mr de Wet said.
Children were discouraged from visiting where possible, to restrict the spread of the virus.
Mr de Wet said the origin of the outbreak was still being investigated.
"It appears that it has started with a patient that has been admitted with the illness but there also appears to be a couple of visitors that had diarrhoea at the same time."
He said the first cases were identified last Monday.
It was unclear whether those were coincidental or if it had started to spread already.
Hospital staff tried to identify patients with such viruses as they were admitted and took appropriate steps to restrict the spread, Mr de Wet said.
The only way to rid the hospital of the virus was to contain affected patients to the same ward and pay particular attention to the hand hygiene of staff and visitors, he said.
Mr de Wet was hopeful the virus would not last much longer.
"It's quite likely there will be a couple more cases," he said.
"What we do is we monitor numbers on a daily basis and put in place all the measures required to prevent the spread.
"At some point you're able to turn it around."
He said staff and visitors to the hospital needed to be particularly thorough about washing and sanitising their hands.
The hospital was asking that visitors visit only one ward, to reduce the risk of spreading the virus.
Middlemore Hospital in Auckland is also battling an outbreak.
A further three patients and three staff are suspected of having the bug at Middlemore Hospital.
If the cases are confirmed it will take the total to 11 staff and seven Middlemore patients with the virus.
Two wards in the hospital are being closely monitored, and people are being asked not to visit patients there if they have been unwell themselves.
Symptoms of norovirus
Nausea, vomiting, abdominal pain, diarrhoea.
What to do if you have symptoms
Stay at home; rest; drink plenty of fluids; be careful with your hand hygiene, especially after going to the toilet; avoid preparing food for others if possible.
If symptoms last more than two days or you have difficulty keeping fluids down, contact your GP or contact Healthline toll-free on 0800 611 116 for advice.