Major Toni Safrudin, the chief of the Ahmad Yani Army Base Security Section, said the accident occurred at around 8:30 a.m.
The aircraft had taken off at about 8 a.m. and was heading back to pick up another student when it crashed, Ankara News Agency said.
The aircraft suddenly fell and was badly damaged, but it did not explode, The Jakarta Post said.
The instructor and a student pilot who were on board suffered minor injuries and were taken to a hospital in the military air base, Safrudin said.
A preliminary report indicated that the helicopter crashed after it lost power, the Post said, but the investigation is ongoing.