The Dornier maritime surveillance aircraft, which was on a routine training sortie, crashed about 25 nautical miles south-west off Goa at around 2208 hours yesterday.
A full-scale search and rescue operation involving nine ships and few aircraft was launched following the crash.
"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.
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.