The remains of one of the Houthi drones that were used in the attack at the King Abdullah Airport in Jazan. (Arab coalition)
It is the second airport attack in less than two weeks blamed on, or claimed by, the Iran-backed Houthi insurgents.
The rebels regularly launch attacks against Saudi Arabia which has for seven years led the military coalition which intervened to support Yemen's internationally-recognized government in the face of Houthi advances.
"A drone launched in the direction of King Abdullah Airport in Jazan was destroyed, with debris falling inside the airport," the coalition said, as reported by the official Saudi Press Agency.
"Sixteen civilians of different nationalities were injured," it said, accusing the Houthis of "again launching cross-border attacks from Sanaa airport".
The airport, and the Yemeni capital city Sanaa, are held by the Houthis, who claimed responsibility for an attack that took place on February 10, also in Saudi Arabia's southwest near Yemen.
Officials in the kingdom said 12 people were hurt on that occasion by falling debris when the Saudi military blew up a Yemeni rebel "bomb-laden" drone targeting Abha International Airport.
In response, the coalition on February 14 said it destroyed a communications system used for drone attacks located near the telecoms ministry in Sanaa.
In December, the coalition said the Houthis had fired more than 850 attack drones and 400 ballistic missiles at Saudi Arabia in the previous seven years, killing a total of 59 civilians.