"We have yet to find him. He is still missing in action," said spokesman Colonel David Obonyo. He said the fuselage of the plane had been burned by al Shabaab after it fell inside territory they control.
The aircraft had been on a combat mission when it came down near the port city of Kismayu, where Kenyan forces are stationed.
One analyst questioned whether al Shabaab had the capability to down combat jets, something it had never managed to do since Kenya began flying missions over Somalia. But he said he could not be certain that al Shabaab had not acquired anti-aircraft weaponry recently.