Around 10 Britons are thought to have been on the boat that capsized into the icy waters after hitting a water fountain near the town of Harstad.
Two boats were carrying 24 people and were returning from a sightseeing trip when one hit the fountain in the harbour at around 2pm GMT.
At least ten Britons have been injured in Norway
But a second boat smashed into the first shortly after the crash.
The Foreign Office said: "We are in contact with the Norwegian authorities following an incident in Harstad. We are ready to support British people affected."
The British group were on a tour with a local travel agent, a company co-owned by a member of the local police in Harstad and a former employee of the force, police said.
Frank Roksøy, editor of the local paper who took pictures of the survivors, told The Sun: "The visitors had arrived the day before on a three or four day vacation.
"They were mainly in their 50s, and this was their first event of the holiday. They were returning from seeing the town by sea when one of the ribs went straight into the fountain.
The Hardsted harbour where the crash took place
"Everyone was thrown into the water, which, of course, was freezing. They were wearing survival suits.
"The other boat came to their aid and they were pulled on board. They were only in the water five or ten minutes.
"Up to five people from the boat could not walk, and there were some broken bones.
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The harbour is close to the Arctic Circle
"There are two regular guys who take the ribs out, but this skipper was new, maybe on one of his first times out.
"We are asking ourselves 'how could this happen in daylight'."
None of the injuries are thought to be life-threatening.
More to follow.