The rescue vessel Siem Pilot arrived at the port of Catania on Sicily on Sunday, after a week patrolling the Mediterranean for stranded refugees.
The 23-year-old sailor was seen leaving the ship at 3.30am on Monday, and has not been seen since.
“They were allowed to leave the ship, and many were out quite late on Sunday,” Ida Dahl Nilssen of Norwegian Criminal Investigation Service (Kripos) told Norway's Dagbladet newspaper.
“He came back with the others, but the last known observation is that he left the ship early Monday morning. A few hours later, it was revealed that he had not come back. We don't know why he left the ship.”
Dahl Nilssen's Kripos colleague Axel Due told the paper that Italian police had already began investigating the disappearance, while other crew members comb the city looking for their missing ship mate.
Siem Pilot was sent to the Mediterranean in May to assist the EU's Triton operation, which rescues refugees attempting to cross the sea.
The ship has suspended its mission to find the missing crew member.
“According to plan, we were supposed to be out on patrol today, but we have suspended it until further notice,” Dahl Nilssen told Dagbladet.
Kripos have no idea where the sailor is, or if he is in danger.
“There are no indications either way. We are keeping an open mind about all possibilities and we hope that he will come back,” he said.