"The crew abandoned the jet," the Russian defence ministry said in a statement, adding that the Tu-95 bomber was not carrying a combat payload at the time of the crash.
Crew members, who were taking part in a training flight outside the far eastern city of Khabarovsk, apparently managed to parachute out, the defence ministry said, citing the crew of a second plane training in the area.
A search was underway for survivors.
"The jet crashed in a desolate area, there is no damage on the ground," the defence ministry said in its statement carried by Russian news agencies.
Over the past weeks, the Russian military has reported a string of accidents that has raised questions about the safety of the country's military aircraft.
In June, the army reported an accident involving a similar TU-95 jet whose engine caught fire during take-off in the far eastern Amur region.
Earlier this month, two pilots of a Sukhoi Su-24 aircraft were killed when it crashed during a training mission in the far east of the country.