The aircraft, believed to be a British-made Tornado, crashed in Saada province this afternoon.
Houthi armed rebels too TV channel al-Massirah they had shot the plane out of the sky.
But Saudi state news agency SPA reported the fighter jet had suffered a “technical fault” while conducting military operations.
The Saudis said a special operation was carried out to evacuate the two pilots, who managed to survive the crash.
A spokesman for the joint coalition forces said: “The Arab Coalition Forces Command implemented a private joint operation to evacuate two pilots in participation of air and land forces where the two pilots were evacuated into the Kingdom’s territories.”
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The Houthis swept across Yemen since 2014 overthrowing the internationally-recognised government of President Abd-Rabbu Mansour Hadi in 2015
The conflict – widely seen as a proxy war between regional rivals Saudi Arabia and Iran – has displaced more than 2 million people, caused a cholera epidemic and pushed the country to the brink of famine.
At least 10,000 people have been killed.
More to follow.