The jellyfish, which usually found in slightly warmer waters than red jellyfish, can give unpleasant stings.
“I can't remember receiving so many reported sightings ever before,” Jan Helge Fosså, a marine biologist at Norway's Institute of Marine Research told Aftenposten.
Fosså said that he expected the jellyfish to follow the currents further north, but was unsure of why numbers had reached such high levels.
Large numbers of blue jellyfish have also been spotted off Sweden's western coast.
Lene Friis Möller, who studies jellyfish at the University of Gothenburg, said that the return of the species was a positive sign of a recovering ecosystem.
“Blue jellyfish are not new, they have existed for a long time, but not in these numbers. The increase in numbers is positive for the environment but not for swimmers,” she told Sweden's Göteborgs-Posten newspaper.
In some parts of Sweden, the numbers of stinging jellyfish are making it near impossible to swim.
“It was insane. There were jellyfish everywhere. I have never before seen so many jellyfish,” Isabelle Packendorff, from Lysekil near Gothenburg, told GT newspaper. ”I'm usually not afraid of jellyfish, but it was daunting with so many of them.”
Although stinging jellyfish are unpleasant, they are important for some sea life.
“The only wildlife we know that depend on stinging jellyfish are tortoise and blowfish. Without jellyfish, they would probably be extinct,” zoologist Petter Bøckmann told Aftenposten.