According to the TASS state news agency, there were also six Russian crew members and three escorts on board the Ilyushin Il-76 aircraft.
It was not immediately clear what caused the crash, which occurred around 11 a.m. Moscow time (0800 UTC). It was also not known if anyone survived the crash.
A special military commission was on the way to the crash site near the border with Ukraine, the ministry said.
There was no immediate official reaction from Ukraine.
Ukrainian media, however, cited military sources as saying that Ukrainian forces downed the plane and that it was transporting missiles.
The Kremlin said in response to a reporter's question that it was looking into the situation.