Officials said there were no injuries and no danger of radiation leaks.
No weapons were on board.
Russian news agencies report that the submarine "Tomsk" caught fire early on September 16 while being repaired at a floating dock at the Zvezda shipyard in Bolshoi Kamen, some 25 kilometers from Vladivostok.
In addition to two firefighting vessels, a ship that monitors radiation levels was reportedly sent to the area as a precaution.
The Russian Defense Ministry has created a special commission to investigate the blaze, which may have been caused by a violation of welding rules.
State-run RIA Novosti earlier quoted an unidentified official at the shipyard as saying the fire broke out after a gas-powered saw was used to cut through a grate, setting a rubber covering, cables, and paint on fire.