The navy said the plane, a Dornier surveillance aircraft, was on a routine flight when it went down late on Tuesday, March 24. The cause is not known.
One crew member was rescued and a search operation has been launched for the missing two, navy spokesman Rahul Sinha said in a statement.
It is the latest in a series of mishaps for the Indian military
Last November, one crew member died and four were missing when a navy ship sank during exercises off the coastal city of Visakhapatnam.
In March 2014, a navy officer died in an accident on board a ship being built at a dockyard in Mumbai.
A month earlier, a fire on board a nuclear submarine off Mumbai left two sailors dead. The navy chief resigned in response.
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