The Russian Investigative Committee said it has initiated "a criminal case" following the crash of the Embraer Legacy aircraft.
Wagner chief Yevgeny Prigozhin was listed among passengers on board.
The committee said the case was based on Article 263 of the Criminal Code of the Russian Federation, which involves the violation of the rules of traffic safety and operation of air transport.
An investigation team is on the way to the scene, it added. "All the necessary forensic examinations will be appointed, a set of investigative actions will be carried out to establish the causes of the crash."