The Dornier maritime surveillance aircraft, which was on a routine training sortie, crashed about 25 nautical miles south-west off Goa coast last night.
The Navy has ordered a Board of Inquiry into the crash.
A full-scale search and rescue operation involving nine ships and few aircraft was launched, the Navy said.
"One survivor has been rescued. Search is on to locate two more officers -- a pilot and an observer," Navy spokesperson Captain D K Sharma said in New Delhi.
The rescued officer, Commander Nikhil Joshi, has been seriously injured in the crash but is stable, Sharma said.
The aircraft is feared to have ditched soon thereafter, it said.
Navy chief Admiral R K Dhowan has rushed to Goa to take stock of the situation.
It is the latest in a series of disasters to hit the navy, and comes just months after a torpedo recovery vessel sank off Visakhapatnam in Andhra Pradesh, leaving five dead.
Eighteen sailors were also killed in August 2013 when INS Sindhurakshak burst into flames in Mumbai harbour.
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