The jet went down near the village of Prostornoye in the Karaganda region Tuesday night, killing the pilot and injuring the navigator, the official Russian news agency RIA Novosti reported.
A statement issued by the Military Prosecutor's Office said the crew managed to eject from the aircraft before it crashed.
The Defense Ministry blamed the crash on a "technical failure" and said it has opened a criminal investigation for "violation of flight rules and flight preparation."
The MiG-31, the world's fastest military aircraft in service, is designed to intercept enemy aircraft at long distances. It is operated by Kazakhstan and Russia.
Celebrity Families of 2014 [PHOTOS]