The Antonov-32 transporter aircraft took off from Chennai (Madras) at 08:30 local time (03:00 GMT), bound for Port Blair in the eastern archipelago of Andaman and Nicobar.
It was scheduled to land at 11:30. A search operation has been launched.
The IAF operates more than 100 Antonov-32 aircraft.
A navy spokesman told the Reuters news agency that surveillance planes and ships were looking for the missing aircraft, which was carrying service personnel to strategic islands near the Malacca Straits, where India has a military base.
India military Antonov plane missing over Bay of Bengal
22 July 2016
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An Indian military plane with more than 20 people on board has gone missing over the Bay of Bengal, the Indian air force (IAF) has confirmed to the BBC.
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