The coalition said in a statement on Wednesday that the wounded were of different nationalities, and included women and children who were taken to a nearby hospital.
It was not yet clear what type of missile was used in the attack. The coalition said the strike proved that the Houthis have aquired "advanced weapons from Iran".
Houthi-affiliated Masirah TV reported that the airport was struck with a cruise missile.
Official Saudi Press Agency (SPA) said that Saudi air defence forces on Monday intercepted the drones that targeted Khamis Mushait in the kingdom's south and caused no damage or casualties.
The rebels said they had targeted the King Khalid airbase near Khamis Mushait.
The attacks come as the Saudi-Emirati coalition has intensified air raids on Houthi positions in the northern Yemeni province of Hajjah.
The rebels have stepped up drone and missile attacks on the kingdom amid tensions between Shia power Iran and the United States, Saudi Arabia's main ally.
Last month, the Saudi air force shot down a bomb-laden drone deployed by Houthi rebels that targeted Jizan airport, close to the southern border with Yemen, the coalition said.
The Saudi-led coalition intervened in Yemen in March 2015 in support of President Abd-Rabbu Mansour Hadi who was forced out of power by the Houthis.
Enduring Saudi raids
Commenting on Wednesday's missile stike on Abha airport, Al Jazeera's Mohammed al-Attab, reporting from the Yemeni capital, Sanaa, said the incident proved the coalition's goal of destroying Houthi's missile capabilities had failed, allowing the rebels to hit back.
"The Houthis … are saying these kind of attacks are revenge for Saudi Arabia’s escalation and their attacks on civilian areas over the past four years," al-Attab said.
"They have killed so many civilians; this brutal war has even targeted weddings, funerals, markets and hospitals," he added.
Hussain Bukhati, a pro-Houthi journalist, told Al Jazeera the missile strike was part of a move by the group to target the coalition with "eye-for-an-eye" attacks, adding Houthi forces in Sanaa still had "many surprise" attacks planned.
Bukhati said a cruise missile was used in the airport strike and claimed it was the second use of such a missile by the Houthis after the group deployed one last year to hit a nuclear power station being constructed in the United Arab Emirates.
The conflict in Yemen began in late 2014 when the Houthis overran the capital and forced the government to flee to Aden.
The Saudi-UAE-led coalition intervened in Yemen in March 2015 in support of Yemeni President Abd-Rabbu 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.
SOURCE: Al Jazeera News