Russia's defence ministry said the incident, which took place at around 6:00 am (0300 GMT), could have been caused by failure of one of the engines of the plane, an Antonov AN-26.
There were six people onboard the aircraft when it made a hard landing at Saratov's Balashov aerodrome, the defence ministry said in a statement quoted by Interfax news agency.
The governor of the Saratov region said in a statement that the servicemen were taking part in a training flight.