The 80-year-old said he did not receive any notification before they left and by this time it was too late to do anything about it as they were well on their way to New Zealand.
"It think people should be told and given the option that if you don't like being exposed to this virus you are allowed to get off. But we found out when we were sea."
Halfway into the 12-day cruise passengers started falling ill and Elisabeth came down with the bug on Saturday night. She was then isolated to her cabin for 48 hours.
"They (passengers) are sick all right. But of course the ship won't tell us how many are sick, but my wife got sick on Saturday night. They are taking all sorts of precautions but it is still happening. They keep telling me, they are doing their utmost and they are doing their best but the fact is it is not effective."
Although his wife had already caught it, the Gibians decided to leave the ship early in Wellington on Tuesday morning because he thought the risk of him still getting ill was still high.
Gibian was told there was no refund but that he may be able to get a credit on a future cruise.
Passengers on the current cruise disembarked in Auckland on Saturday and the couple is worried new passengers will board oblivious to the ship's recent norovirus history.
In a statement, Celebrity Cruises confirmed there had been some reported cases of gastro-intestinal illness symptoms among the 3985 guests and crew onboard and that guests on previous cruises had also come down with the same thing.
"Those affected by the short-lived illness are being treated by the ship's doctors and responding well to over-the-counter medication."
The company said the cases were "a reflection of the numerous reports of such illnesses in the community in recent months".
Despite Gibian's claims passengers were not told prior to boarding, Celebrity Cruises said they sent a text message informing them boarding had been delayed so staff could do more cleaning and sanitisation of the ship due to cases of illness.
Passengers booked on the next Celebrity Solstice cruise due to leave Auckland on Saturday would be given the same advice and more crew, including housekeeping and medical staff, were being added to help with the comprehensive sanitation programme, the statement said.
Celebrity Cruises said it was taking a number of actions to prevent further contamination, including covering buffets, providing hand sanitiser around the ship and cleaning and sanitising the ship when guests embarked for the day and at its home ports in Sydney and Auckland. It was following advice from health experts that the best defence against stomach viruses was to wash hands and educating passengers about this.
This is not the first time passengers on a cruise ship have come down with norovirus. In 2014, the Herald reported that 60 of 2670 passengers on a 12 day cruise aboard The Diamond Princess from Australia to New Zealand caught the violent stomach bug.
How Norovirus spreads:
• Consuming contaminated food or drinks
• Touching contaminated surfaces or objects and then putting your fingers in your mouth
• Having direct contact with an infected person (eg, by sharing food or eating from the same plate or cutlery)
• Through the air (when vomiting sends tiny particles into the air)
Symptoms:
• Nausea
• Vomiting and diarrhoea
• Stomach cramps
• Headache
• Low-grade fever
• Chills
• Muscle aches
Treatment:
• Drink plenty of fluids such as plain water and oral rehydration drinks
• Don't take medicine to stop vomiting or diarrhoea
Source: Ministry of Health