At least two people died on the ground when the plane came down in a village, hitting houses before skidding into a rice field where it caught fire.
The plane had been flying from Jakarta to eastern Java when it crashed.
Visibility appears to have been good and there is no indication yet of what caused the crash.
It missed landing at Iswahyudi air force base and struck houses in the village of Geplak, 4km away, at around 0630 local time (2330 GMT).
Initial reports say the last contact with the crew was a few minutes before the plane came down, as it was making its final approach to land.
The C-130 Hercules had been carrying about 110 passengers and crew. At least 10 children were reported to have been on board.
TV pictures showed soldiers with stretchers trying to evacuate casualties from the scene. Reports say the site is difficult to reach because it is on the edge of a rice field.
"About 15m of the tail is still intact but the body to the front is broken and burnt," said a local official in the district of Magetan.
Witnesses spoke of hearing a large explosion while the plane was still in the air, and then seeing it split apart.
"One of the wings fell off," a local villager was quoted as saying on the Kompas newspaper's website.
"Then the plane nose-dived into the houses."
The location of the crash is near the border of the districts of Madiun and Magetan, about 150km south-west of Indonesia's second-biggest city, Surabaya.
Air force accidents
Indonesia's air force has long complained of being underfunded and handicapped by a US ban on weapons sales, correspondents say. The ban has recently been lifted.
It has suffered a series of accidents, including one involving a Fokker 27 plane that crashed into an airport hangar in western Java last month, killing all 24 aboard.
An Indonesian air force Hercules overshot the runway at Wamena airport in Papua on 10 May. One person was reportedly injured in that incident.
In response, the air force said it would check its Hercules fleet, which is being upgraded with airframe and engine capability improvements.
There have also been a number of commercial airline crashes in Indonesia in recent years which have killed more than 120 people.
In 2007, all Indonesian airlines including national carrier Garuda were banned from the European Union, being deemed unsafe.