The crew members were poisoned by fumes when the vessel caught fire while taking biometric measurements on Monday, the defence ministry said.
The vessel was based at Severomorsk, in the Murmansk region, which is the main base of the Northern Fleet.
An investigation into the incident has begun under the commander-in-chief of the navy, the ministry added.
A submersible is an underwater vessel which differs from a submarine in that it usually requires a support ship on the surface. A submarine is fully autonomous.
The Kursk submarine, which was destroyed by an explosion in the Barents Sea in August 2000 with the loss of its crew of 118, also belonged to the Northern Fleet.