The submariners died from smoke inhalation after a blaze broke out on the craft, which was carrying out research in Russian territorial waters, according to the state-run news agency Tass.
The fire was later extinguished, Tass reported, hailing the "selfless actions of the team" on board.
The submersible, which is smaller than a submarine and has limited power reserves, is now at the naval base in Severomorsk on the Barents Sea.
An investigation into the incident is being carried out by the Russian navy's commander-in-chief, state news agency RIA-Novosti reported.
Russian President Vladimir Putin has called for Defense Minister Sergei Shoigu to oversee the probe, Tass reported.
"I ask you to fly to Severomorsk in order to personally listen to the reports and to aim the commission to get to the bottom of the causes of the tragedy," Putin told the defense minister, per Tass. "I ask you to report to me personally upon your return."
The blaze is one of the deadliest incidents the Russian navy has experienced in years.
Twenty people were killed on board a Russian nuclear submarine in 2008, when a fire extinguishing system was triggered accidentally. In 2000, more than 100 men died on a nuclear-powered submarine when two explosions in its bow sank it to the floor of the Barents Sea.
This is a developing story.