Earlier on Wednesday, the Houthi rebel group claimed responsibility on targeting the Abha airport by a cruise missile, saying that the missile "hit the target accurately".
The list of injured passengers includes three Saudi, Yemeni and Indian women and two Saudi children.
The colonel said eight cases had been transferred to hospital to receive treatment for moderate injuries.
Saudi Arabia's civil aviation authority said on Wednesday afternoon that air traffic had returned to normal at the airport.
Houthi-backed Al Masirah TV announced the attack and claimed the rebels had targeted the airport with a cruise missile.
"This attack also proves this terrorist militia's acquisition of new special weapons; the continuation of the Iranian regime's support and practice of cross-border terrorism; and the continued violation of relevant U.N. Security Council resolutions", said Almalki. The coalition said the attack proved that the Houthis have acquired "advanced weapons from Iran".
The Saudi-led military coalition has vowed to respond firmly to the attack at the Abha airport.
Dr. Mishaal Al-Sulami, Speaker of the Arab Parliament, considered the terrorist cowardly attack a war crime.
In a reference to the US atomic bombs dropped on Japan during World War II, one hard line newspaper in Iran, Farheekhtegan, or Educated, published a photo of a mushroom cloud with the headline "How Can You Trust a War Criminal, Mr. Abe?".
"We must condemn these violations and hold the global community responsible for failing to support and help the government to battle the militias".
There has been a spate of cross-border attacks by the rebels in recent weeks which have coincided with reports of intensified coalition strikes on rebel strongholds on the other side of the border.
Riyadh accused its regional arch foe Iran of having a hand in that attack and it levelled a similar allegation over the airport strike.
War erupted in Yemen in 2014 after Houthi rebels drove the internationally recognised government of Mr Mansur Hadi from the capital, Sanaa, leading to the worst humanitarian crisis in the world.