An air strike by the Saudi-led coalition that killed dozens of people in Yemen last August was branded an apparent war crime by Human Rights Watch.
"Targeting Abha airport proves that the Houthis have obtained advanced weapons from Iran", the coalition statement said, saying the attack could amount to a war crime.
The Houthis earlier on Wednesday claimed they'd launched a cruise missile at the Abha airport.
Houthi-run Masirah TV reported that the militias targeted the Abha International Airport with a cruise missile.
A military spokesman threatened on Tuesday that the group would target every airport in Saudi Arabia and that the coming days would reveal "big surprises".
The kingdom is participating in a three-year military campaign in Yemen - which has become nearly a proxy war with Iran. The conflict has resulted in a massive humanitarian crisis in the war-torn country. A Saudi-led coalition has been carrying out airstrikes against the Houthis at Hadi's request since March 2015.
It has triggered what the United Nations describes as the world's worst humanitarian crisis, with 24.1 million - more than two-thirds of the population - in need of aid.
Alarmed by the rise of a group they believed to be backed militarily by regional Shia power Iran, Saudi Arabia and eight other mostly Sunni Arab states began an air campaign aimed at restoring Mr Hadi's government.
Iran has been the focus of global attention today as the US President scrapped the deal preventing Tehran from pursuing nukes.
Twenty-six people have been injured after Yemeni rebels attacked an airport in Saudi Arabia.
Two oil pumping stations in Saudi Arabia were targeted by Houthi drones in May causing supply disruption.
The latest attack, which is yet to be confirmed by the Saudis, comes a day after Riyadh said it intercepted two drones fired by the Iran-aligned group, which controls a large part of Yemen, including the capital Sanaa.
Arab Coalition commanders have said there has been a signficant increase in the sophistication of the weapons used by the Houthis.