Eighteen people were treated at Abha International Airport for minor injuries and another eight were taken to hospital, Turki al-Malki, spokesman of the US-backed Saudi-led coalition battling rebels in Yemen, said in a statement published on Saudi state media.
"Three women, a Yemeni, an Indian and Saudi and two Saudi children were amongst those injured," al-Malki said, adding that "authorities are working on identifying the type of missile that was used in this terrorist attack."
According to Houthi-run Saba News, a strategic guided cruise missile was used in the attack.
"In light of these terrorist and immoral transgressions by the Houthis, the coalition will take strict measures urgently and carefully to deter them," al-Malki said. "This includes protecting civilians and civilian assets. The terrorist elements responsible for planning and carrying out this attack will be held accountable."
The airport, which services flights within Saudi Arabia, as well as to Egypt and the United Arab Emirates, suffered from material damage, al-Malki said.
The war in Yemen began in early 2015 when Houthi rebels -- a minority Shia group from the north of the country -- drove out the internationally-recognized government and forced its president, Abdu Rabbu Mansour Hadi, to flee.
The crisis quickly escalated into a multi-sided war, with neighboring Saudi Arabia leading a coalition of Gulf states against the Houthi rebels. The coalition is advised and supported by the US, among other nations.
Wednesday's attack comes after Saudi Arabia reported that "armed drones" had attacked two pumping stations in the kingdom in May.
That came just a day after Riyadh said two of its oil tankers were sabotaged off the coast of the United Arab Emirates.