The trainee pilot managed to eject safely from the aircraft, which crashed inside INS Hansa base while it was trying to take off.
The incident led to operations at the Goa airport being suspended from 12.30 pm to about 1.40 pm.
Goa's Dabolim airport is located inside the naval base.
In a statement, the Navy said in New Delhi that a Board of Inquiry (BoI) had been ordered to investigate the cause of the accident.
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During deceleration, the aircraft veered off the end of runway and caught fire. The pilot jettisoned the canopy and egressed the aircraft safely, it added.
The Navy said the fire was expeditiously doused by the safety services.
"The runway at Goa was cleared and services were restored expeditiously," it said.
"When the pilot was taking off, there was some malfunction in the aircraft which we will have to investigate," Real Admiral Punit K Bahl, Flag Officer Commanding Goa Area (FOGA), told PTI.
There was little fire and smoke at the aircraft, which was brought under control.
"This is the first main incident of the MiG 29K since the time it was inducted," Bahl said.
"It is too premature to say whether this washuman or machine error, because we have to investigate, which will take some time," he added.
According to Goa airport director B C H Negi, the incident happened 10 minutes before a civilian aircraft was scheduled to land.
The Russian-made MiG 29K was inducted in the forces on May 11, 2016 after the decommissioning of the Sea Harriers.
Eyewitnesses said the aircraft veered off the runway before it could take off.