There have been six other Russian air force crashes in recent weeks.
The two-seat gunship was performing stunts and firing flares with three other helicopters. It then began to spin rapidly, before falling to the ground and bursting into flames.
Its pilot Lt Col Igor Butenko was killed. His son told Russian media that the accident was not due to pilot error.
"There are situations when it's impossible to survive no matter how well-trained the pilot is," he told Lifenews.
The Russian defence ministry says the condition of the other pilot's condition is "satisfactory".
There were no injuries to spectators at the air show.
An investigation has been launched into the cause of the crash, although the surviving pilot has said that a hydraulic failure was the cause. The country's fleet of Mi-28s will remain grounded until the investigation is completed.
The Mi-28 is an attack helicopter widely used in Russia, as well as countries such as Iraq and Kenya.
At least five people have been killed in recent military aviation crashes.
In the past few years, the air force has received hundreds of new helicopter and planes as part of a programme to modernise and reequip Russia's military.