The unnamed deceased was a 59-year-old man from Gothenburg, Sweden. He was joined aboard the boat by four Swedish tourists and a Norwegian guide.
The Norway North sea rescue team was alerted after a Mayday message was received at 1pm on Sunday and sent out eight rescue boats.
Five survivors and the dead man were pulled from the water and taken aboard rescue vessel "Barents Explorer."
"We found the people in the water and understand the boat took in water and sank," said rescue leader Finn Tore Sortland to Finnmarken.no.
A SeaKing rescue helicopter arrived at the scene shortly after. A rescue man and a physician were hoisted down onto the rescue boat to help the surviving victims and followed the boat in to land.
The five survivors were treated by medical staff on land in Mehamn. No one was admitted to hospital.