The submarine's nuclear reactors had been shut down and posed no danger, officials said. However, nine people were injured when fighting the fire and taken to hospital.
Television pictures showed a plume of black smoke above the yard in the Murmansk region of northern Russia as over 100 firemen struggled to put out the flames which witnesses said rose 10 metres (30 feet) above the Yekaterinburg submarine.
"The fire has been localised," Emergencies Minister Sergei Shoigu told officials leading the firefighting effort from an emergencies control room in Moscow, more than nine hours after the blaze began at 1220 GMT Thursday.
Shoigu's comments indicate the fire was still burning but that efforts to sink the submarine partially at the dock had succeeded in reducing the intensity of the flames.
"There are no open flames. A fire crew is still at the scene pouring water over the outer hull as well as the space between the inner and outer hulls of the submarine," said an unnamed Defense Ministry source, speaking to Interfax.
The governor of the Murmansk region, Dmitry Dmitrienko, said the submarine's two nuclear reactors had been shut down. All weapons had been removed from the 167-metre (550 feet) Yekaterinburg, which launched an intercontinental ballistic missile from the Barents Sea as recently as July.
"Radiation levels are normal," a spokeswoman for the Emergencies Ministry said.
A law enforcement source told Russian news agencies that seven servicemen at the shipyard and two Emergencies Ministry personnel had been injured when trying to put out the fire and had been hospitalised. Interfax reported they had suffered from the effects of smoke.
After hours of trying to put out the flames, officials decided to submerge the 18,200-tonne submarine partially at the Roslyakovo dock, one of the main dockyards of Russia's Northern Fleet, 1,500 km (900 miles) north of Moscow.
Local media reports were vague, but the blaze was believed to have started when wooden scaffolding caught fire during welding repairs to the submarine, which had been hoisted into a dry dock.
The submarine can carry 16 ballistic missiles, each with four warheads. Russian submarines' reactors are built to withstand enormous shocks and high temperatures.
The Yekaterinburg is a Delta IV class submarine. Russia's Northern Fleet was established under the Soviet Union to watch over European waters and was armed during the Cold War against threats from NATO.
Russia's worst post-Soviet submarine disaster occurred in August 2000 when the Kruse nuclear submarine sank in the Barents Sea, killing all 118 crewmen aboard.
President Dmitry Medvedev and Prime Minister Vladimir Putin have been informed about the incident, said Deputy Prime Minister Dmitry Rogozin, who oversees the military.