'Toll to rise'
At least 14 children, familiy members of military personnel, were believed to have been on the flight.
Two people on the ground were also killed, Bambang Soelistyo, an air force spokesman, said.
Officials have said they expect the death toll to rise once they are able to sift through the wreckage.
About 15 injured people had been sent to local hospitals, many suffering from bad burns, Indonesian media reports said.
The Hercules aircraft was flying from Halim airbase near Jakarta, the Indonesian capital, to a base near Madiun when it came down.
The weather was clear at the time of the crash and investigations have begun into the cause of the disaster.
An eyewitness named Tofa told Indonesia's Metro TV news channel that he had heard two explosions as the plane crashed in flames.
He said local residents immediately ran to help pull passengers from the burning wreckage.
Other witnesses reported seeing the plane split apart in mid-air following a loud explosion.
Indonesia's air force has long complained of being underfunded and handicapped by a US ban on weapons sales, which had recently been lifted.
The air force has suffered a series of accidents, including one last month involving a Fokker 27 plane that crashed into an airport hangar, killing all 24 on board.
Last week a Hercules aircraft lost a wheel after it overshot the runway as it came in to land in the eastern Indonesian province of Papua.
Recent years have also seen a series of deadly crashes involving commercial passenger planes, and Indonesian airlines are currently banned from European Union airspace over safety concerns.