The Russian-made AN-32 was on its way to Port Blair, the capital of India's Andaman and Nicobar chain of islands, from the southeast city of Chennai when it disappeared from radar on Friday.
There were 21 military personnel on board including six crew.
The other people on board were civilians, some of them family members of soldiers deployed on the islands.
"It was a routine courier mission to Port Blair, the plane was airborne at 8:30am and due to land at 11:30," air force spokesman Wing Commander Anupam Banerjee said.
India has been beefing up its military presence in the Andamans in recent years.
The islands are near the Malacca Straits, one of the world's busiest shipping lanes which link the Indian Ocean to the South China Sea and East Asia.
The defence ministry said four surveillance planes, 12 ships and a submarine were searching for the aircraft in one of India's largest search and rescue operations in recent years.
The plane went missing about 300 km (186 mile) east of Chennai, the ministry said in a statement.
The Andamans are about 750 nautical miles from mainland India.
The defence ministry said the submarine had been deployed to locate transmissions from an emergency locator beacon on the AN-32 aircraft.
The plane is a workhorse of the air force, chosen for its ability to operate from short runways.