The aircraft crashed Friday night at Dhana in Sagar district, about 188 km east of Bhopal, the capital city of Madhya Pradesh.
"Last night at around 9:30 (local time), a single-engine trainee aircraft of the Chimes Aviation Academy (CAA) crashed here in an agricultural field close to Dhana airport," a police official posted in Sagar said. "Two people, instructor, Ashok Makwana and trainee pilot, Piyush Chandel, were killed in the crash."
Officials said the area was covered with fog at the time of the crash.
The aircraft took off late Friday in the evening as part of the night training for the trainee pilot.
"Preliminary investigations reveal the trainee pilot attempted landing on airstrip but it landed in a nearby farm field because of very poor visibility," the police official said, adding that a thorough investigation would be carried out.
Madhya Pradesh Chief Minister Kamal Nath expressed grief over the death of two people in the aircraft crash and offered condolences to families of the deceased.