The submarine is undergoing maintenance at a plant in Russia's far eastern Primorye Territory, RIA Novosti reported.
The fire was sparked by welding operations, which ignited rubber insulation and old paint inside the vessel's main ballast tanks, the report said.
Several firefighters were allowed to go home after being treated for mild carbon monoxide poisoning, said a spokesman for the Zvezda plant, where the submarine was undergoing maintenance.
The spokesman said the blaze wasn't likely to cause an explosion on the submarine but 10 fire brigades were at the scene as a safety precaution.
The submarine was docked in 2010 because of problems with the cooling engine of its nuclear reactor, RIA Novosti said.