Reports on Monday said the L-39 flight trainer crashed in poor weather conditions during a routine training flight in the Volgograd Region. The flight instructor died in hospital, and the cadet is in intensive care.
"The preliminary cause of the crash is poor organization of training flights," Colonel Alexander Drobyshevksy said.
Drobyshevsky said the investigation is continuing as the plane's black box recorders have been taken away for study.
Russia's Air Force Commander Alexander Zelin visited the crash site on Monday night.
The Czech-made L-39 Albatross is designed for initial and advanced training. It was a standard jet trainer for the Soviet Union and other Warsaw Pact countries.