Derek and Esther Browne, from Hampshire, were two of 200 Britons on board the ship which evacuated 1,300 passengers and crew members after losing power and sending a mayday call in treacherous conditions.
Mr Browne told BBC Radio 5 Live’s Stephen Nolan: “We had a few people on stretchers, several with cuts, two with broken limbs, but fortunately we were alright.
“We were airlifted onto the helicopter which was quite a frightening experience.”
He added: “I’d never been in a helicopter before, there were a lot of high winds, hovering overhead and the winchman came down and we were then collected up and so I shut my eyes as we arrived into the helicopter and there were 15 of us for about a 20-minute ride.”
Mr and Mrs Brown said “the whole boat was swaying, it was very rough” when they were airlifted to safety.
Dramatic footage shared online shows the ship rocking and debris falling from the ceiling while passengers were waiting to be rescued.
According to police in Moere og Romsdal, the ship’s crew anchored in Hustadvika Bay as they were concerned the ship would get stuck in the high winds.
Following the evacuation, 16 people were taken to hospital – three with serious injuries – and 230 people were registered at a reception centre, authorities said.
A spokeswoman for Viking Cruises said: “The ship is proceeding on its own power and a tugboat is on site. The evacuation is proceeding with all necessary caution.
“A small number of non-life threatening injuries have been reported. Guests are being accommodated in local hotels when they arrive back on shore, and Viking will arrange for return flights for all guests.”
According to Norwegian media, the majority of the cruise ship passengers were British and American tourists.
The ship was visiting the Norwegian towns and cities of Narvik, Alta, Tromso, Bodo and Stavanger and it was scheduled to arrive on Tuesday to the port of Tilbury in Essex.
A spokeswoman for the Foreign Office said: “We are in touch with Norwegian authorities and stand ready to help any British people who require our assistance”.