The attack was carried out with the use of unmanned aerial vehicles, the Al Masirah broadcaster reported.
That was the fourth Houthi attack on the Abha airport in a week. On Wednesday, a Houthi rocket hit the arrival lounge of the airport, leaving 26 people injured.
Yemen, a small nation in the south of the Arabian peninsula, has been engulfed in an armed conflict between the government forces, led by President Abdrabuh Mansour Hadi, and the rebel Houthi movement for several years. The Saudi-led coalition has been carrying out airstrikes against the Houthis at Hadi's request since March 2015. The conflict has resulted in a massive humanitarian crisis in the war-torn country.