"Before 2013 is over, all mosques in Norway [will] be burned to the ground," an unnamed group of extremists wrote in an email to the World Islamic Mission Mosque in Oslo.
The outfit added: "We are a group of men who have planned this for seven years."
It is unclear if the latest anti-Muslim threat is related to the three-day siege in the upscale Westgate mall in Nairobi.
Experts are not certain if the threat is serious enough.
"I think this is just some crazies who want attention," said Ghulam Sarwar, chief of an international Muslim organisation named Jamaat Ahle Sunnat.
Norway has been receiving such anti-Islam threats in recent days and the latest one is likely to be part of it, suggest reports.
The Oslo police have held an emergency meeting with Norway's Islamic Council following the threats.
When the Kenyan siege began, anti-Muslim campaigners severed a pig's head and kept it outside Norway's largest mosque in Oslo enraging scores of Islamic followers.
"Many people were very angry and I am also angry. I would never do something like that to others where they pray. They are insulting other peoples' religion," said Mohamed Hassan, a Somali-Norwegian, according to daily The Local.
Norway was rocked when anti-Islam mass killer Anders Breivik went on the rampage claiming 77 lives during a bomb and gun attack in 2011.