The Mi-28N attack helicopter was participating in the show as part of a competition organised by the Russian defence ministry, Russian media reported from the event.
“One pilot has died, the condition of the other is satisfactory,” the ministry said in a statement published by Russian news agencies.
The Russian airforce proceeded to ground all Mi-28 flights after it was revealed that the crash could have been caused by equipment failure.
The air show Aviadarts, where airforce plane and helicopter crews compete to carry out timed tasks, was suspended for the day.
Television footage showed rescue workers attending to the smouldering helicopter lying on its side in the airfield after it crashed and burst into flames.
The defence ministry said the accident was apparently caused by a hydraulic system failure, which was reported by the surviving pilot who ejected from the chopper.
“According to the second pilot, the catastrophe happened due to aviation equipment failure,” said commander of Russian airforce Viktor Bondarev. “I have stopped all flights on Mi-28” until an investigation is complete.
The Soviet-designed Mi-28 has been used by the Russian airforce since the mid-2000s and is also exported to a number of countries including Iraq.
There have been at least six incidents over the past few weeks involving Russian military planes and helicopters.