Hundreds more passengers who travelled on the MS Roald Amundsen are in quarantine and awaiting test results, the company that owns the ship said.
The ship, which belongs to the Norwegian firm Hurtigruten, docked in the port of Tromso in northern Norway on Friday.
Hurtigruten has halted all leisure cruises because of the outbreak.
"This is a serious situation for everyone involved. We have not been good enough and we have made mistakes," Chief Executive Daniel Skjeldamsaid in a statement on Monday.
"A preliminary evaluation shows a breakdown in several of our internal procedures," he added. "The only responsible choice is to suspend all expedition sailings."
Norway's government has announced it will stop all cruise ships with more than 100 people on board from disembarking passengers for at least 14 days.
And police said they were investigating whether any laws had been broken prior to the outbreak on the Roald Amundsen. "We have found grounds to open a case," a police official told Reuters news agency.
The MS Roald Amundsen had been on a week-long voyage to Svalbard in the Arctic, and was also reportedly scheduled to visit ports in England and Scotland in September.
Four crew members were admitted to hospital on Friday with coronavirus symptoms, shortly after the ship docked in the Arctic port of Tromso, and they later tested positive for the virus.
Another 32 crew members on board were found to be infected. The staff who tested positive included German, French and Filipino citizens.
They were tested for the virus before leaving their home countries but did not quarantine before starting work on the ship, Hurtigruten said.
Almost 180 passengers were allowed to depart the ship on Friday, leaving the authorities scrambling over the weekend to locate and test those who had been on board.
All the passengers have now been contacted and told to self-isolate for 10 days, health officials said. Five passengers have so far tested positive out of 387 who had travelled on the ship since 17 July.
"We expect that more infections will be found in connection to this outbreak," said Line Vold, a health official.