Sergei Shoigu said radiation monitoring would also now go back to normal after being stepped up when the blaze started on wood decking near the Yekaterinburg.
Officials said there was no risk as its two reactors had been shut down. Nine people were hurt fighting the fire.
President Dmitry Medvedev has ordered an investigation into the incident.
One of his deputy prime ministers has promised that the Yekaterinburg, a Delta-IV-class nuclear submarine, will be repaired within several months.
"According to preliminary information, the damage caused by the fire will not affect the ship's combat characteristics," Dmitriy Rogozin said.'No radiation threat'
The Yekaterinburg had been inside a dry dock at the Roslyakovo shipyard - on the Barents Sea coast, 1,500 km (900 miles) north of Moscow - on Thursday when wooden scaffolding around it caught fire.
The blaze soon spread to the submarine's rubber-coated outer hull.
Television pictures showed thick smoke billowing from the top of the vessel as 11 fire crews doused the flames with water from helicopters and tug boats. The submarine was later partially submerged in an effort to extinguish the blaze.
The fire was contained at 01:40 on Friday (21:40 GMT on Thursday), according to the emergency situations ministry, but by the morning, the submarine was still smouldering, and firefighters were still working at the scene, pouring water over the outer hull as well as the space between it and the inner hull, reports said.
A law enforcement source told Russian news agencies that seven servicemen at the shipyard and two emergency ministry personnel had suffered from smoke inhalation.
On Friday afternoon, Mr Shoigu told a meeting of officials the fire had been "put out completely", and that there was "no open burning".
He said that the cooling of the submarine's hull would continue.
Mr Shoigu also said that "the heightened regime of monitoring the radiation situation" on board and in the surrounding area would be lifted.
Earlier, officials insisted the submarine's two nuclear reactors had already been shut down and that radiation levels on board and in the area were normal.
"These parameters are within the limits of natural radiation fluctuation levels. There is no threat to the population," the emergency ministry said.
The vessel's 16 inter-continental ballistic missiles, each with four warheads, had also been removed when the repair work began, officials said.
Some of the crew remained on board the submarine during the fire to monitor temperatures and carbon dioxide levels, they added.
The Russian Navy's Commander-in-Chief, Adm Vladimir Vysotskiy, and Chief of the Navy Staff Adm Aleksandr Tatarinov are at Roslyakovo to oversee the operation.
Safety on Russian navy submarines is a sensitive issue for the military following the Kursk disaster in August 2000.
The Kursk nuclear submarine sank in the Barents Sea off north-west Russia, killing all 118 seamen on board. Investigators concluded that an explosion of fuel from one of its torpedoes caused the sinking.