The airline's press service said in an email Sunday that Fileva, 55, was aboard a single-engine, six-seat Epic-LT aircraft that crashed in a field on approach to the small airport at the town of Egelsbach in southwestern Germany about 3:30 p.m.
German aviation authorities were probing the cause of the crash.
Business publication Forbes.ru estimated Fileva's fortune at $600 million.
German police say a pilot and two passengers are believed to have died in the crash of a small airplane near Frankfurt and two more people died in a collision with a police vehicle responding to the scene.
Police said the six-seater airplane took off in France and was on its way to the central German town of Egelsbach when it crashed and burned in a field Sunday afternoon near Erzhausen, 10 kilometers (6 miles) south of Frankfurt.
Police said they believed three people were aboard but were still working on positive identification of the victims as well as confirming the number of occupants.
The dpa news agency, citing police, reported that three people in a police vehicle were seriously injured in the traffic crash while the two people in the other car died.