"An explosive-laden drone sent by the terrorist Houthi militia to target Najran airport" was intercepted and destroyed by the Saudi air force, coalition spokesman Colonel Turki al-Maliki was quoted by state media as saying.
The Yemeni rebels' Al-Masirah TV said the attack - the third against Najran airport in 72 hours - had targeted a Patriot air defence system.
Maliki said "the rebels attacked a civilian airport" and warned of a "response".
An armed drone sent on Tuesday had hit a weapons depot at the same airport, setting off a blaze, according to Al-Masirah.
Maliki said on Tuesday that the rebels attacked a "civilian installation" in Najran province bordering Yemen with an explosives-laden drone, but did not report casualties.
The Saudi-led coalition intervened in Yemen in March 2015 to push back an advance by the Iran-backed Houthi rebels, who continue to hold the capital Sanaa, and to restore to power President Abedrabbo Mansour Hadi.
Since then, the conflict has killed tens of thousands of people, many of them civilians, relief agencies say.
It has triggered what the UN describes as the world's worst humanitarian crisis, with 24.1 million - more than two-thirds of the population - in need of aid.
Follow us on Twitter: @The_NewArab