Both planes took off from the Gwalior airbase on Saturday morning, about 50 kilometres (30 miles) east of where they crashed.
“In the Pahadgarh forests, we found the wreckage of one of the planes and an injured pilot,” officer Dharmender Gaur told AFP.
“The other plane is likely to have fallen further away from the site, and we have dispatched teams to find it.”
Meanwhile, local administrator Ankit Asthana told Reuters that two of the three crew members from one of the planes had been rescued and taken to hospital.
The third crew member’s condition was not immediately known, and no information was released about the crew of the second plane.
According to ANI news agency, the aircraft that crashed in India’s Madhya Pradesh state were a Sukhoi-30 and a Mirage 2000.
The accident on Saturday is the latest in a series involving India’s military air fleet.
Last October, five army soldiers were killed when their helicopter crashed in Arunachal Pradesh, near the country’s militarised and disputed border with China.
