The armed forces said in a short statement that the jet taking part in the fighting was "lost," Reuters reported.
Riyadh and a coalition of Arab states entered Yemen's civil war a year ago, in an attempt to restore fugitive ex-President Abd-Rabbu Mansour Hadi after Houthis ousted him from power.
There was no immediate comment from the Saudi-led coalition.
At least two jets from the alliance have crashed since the start of the campaign.
In May 2015 a Moroccan F-16 warplane crashed while on a mission with the alliance in Yemen, and the Houthi militia said tribesmen had shot down the aircraft.
In December that year a Bahraini F-16 jet from the coalition crashed in Yemen's neighbor, Saudi Arabia, after suffering from a technical fault.