Coalition officials say the parking lot at the Abha airport, which services a resort, was hit. It gave no other details including whether it was struck by a missile or a drone.
The Houthi rebels say they flew drones over the Abha and Jizan airports, but the Saudis did not confirm Jizan was also targeted.
A Houthi missile struck Abha last week, wounding 26. Human Rights Watch condemned the attack as a possible “war crime” and the Saudis promised to take “stern action.”
The Saudi coalition is helping the Yemeni government try to push the Iranian-backed Houthis out of the capital, Sana’a.
While Iran admits support for the Houthis, it denies Saudi allegations of arming the rebels.
A diplomatic quartet made up of Britain, Saudi Arabia, the United Arab Emirates, and United States issued a statement Sunday condemning the Houthi attacks on the airports and what it calls Iranian “destabilizing activity” in Yemen and elsewhere in the Middle East.
The statement demands Houthis end all restrictions on food and emergency aid deliveries in Yemen and allow the World Food Program to get back to work.
While the quartet’s statement makes no mention of Saudi-led airstrikes in Yemen, which have killed thousands of civilians, it urges all parties to accelerate implementation of the December ceasefire agreement. The statement says the quartet remains committed to the peace process and Security Council resolutions concerning Yemen.
The Saudi coalition and rebels agreed at Stockholm in December to a military withdrawal from southern Yemen, including the key ports of Hodeidah, Ras Issa, and Saleef.
While the rebels have started pulling back from the ports, the Saudis say they will not do so until the U.N. can verify the Houthis have fully kept their side of the bargain.
The Houthis accuse the coalition of stepping up airstrikes on their positions in northern Yemen, prompting retaliatory airstrikes on Saudi territory.