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.”
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.