The tusk was removed from a skeleton near Rubypynten in Recherchefjorden.
"We were there with the round cruise on Saturday, Sept. 6," said Arild Lyssand, a police chief inspector for the governor. "Then we should have picked up the remains that were supposed to be for the museum, but the tooth was missing."
According to Lyssand, a subsequent report indicates the skeleton was intact during the second half of July, but the tooth was missing in early August.
The governor is now investigating the matter and is seeking tips from the public to find out what happened.
Narwhals have a large spiraling tusk from a protruding canine tooth that can be more than two-and-a-half meters long.
The whale skeleton in Recherchefjorden should have gone to Svalbard Museum, which had been allowed to take it into their collection.
"We think it is a great pity that people take things that should benefit society," said Sander Solnes, the museum's curator.
He adds the narwhal is a rare animal and it is rarely possible to find dead specimens on land since they often sink.
"It would be very interesting and important for science that we have an example of such an animal as well," he said.
Svalbard Museum has a cultural history magazine, while the Natural History Museum in Oslo is responsible for all natural history material in Svalbard.
"We nevertheless want to have a study collection of a representative sample of animals living in Svalbard," Solnes said.
It was in this collection the narwhal skeleton would have fit.
"The magazine we use actively in providing a context for those wondering about something specific and for school classes," Solnes said.
He said he fears it now will take several years before the appearance of another skeleton that is intact.
"It is a great pity it has not gone to the common good," he repeated.