The pilot survived and has been hospitalized, RIA Novosti reported.
Heavy fog in the vicinity of the Khankala military base has been blamed for the crash of the Mi-8 helicopter.
Only crew members were aboard the craft at the time of the crash, said the official, who spoke on condition of anonymity.
It was the second helicopter crash in Russia in two days.
An Mi-8 crashed on takeoff Friday when its rotor blade hit the ground in the city of Khabarovsk. No one was injured, but crew members face prosecution for violating flight rules, investigators said.