It reported the rebels saying the missile was sacked in response to "Saudi-American aggression and crimes against the people of Yemen".
Passengers at the airport, which British Airways flies direct to from the United Kingdom, said they heard an explosion.
Saudi Arabia's air forces announced on Saturday they had intercepted a missile targeting Riyadh from Yemen, Al Arabiya local news reported. Earlier reports said there was an explosion at the airport.
Media tied to Yemen's Houthi rebels, including al-Masira, claimed a short-range Burkan H2 missile was sacked in response to "Saudi-American aggression and crimes against the people of Yemen". The missile was allegedly aimed at the King Khalid International Airport.
Saudi Arabia is leading a military campaign against the rebels.
Uber, Lyft ban far-right activist for anti-Muslim rant
She added: "The two women were smiling or smirking in hijabs as they walked past scene of terrorist attack". The full e-mail was shared on Twitter via the New York Times' Mike Isaacs.
Al-Qahum was referring to airstrikes this past week on a hotel and a market area in Yemen's northern province of Saada.
Yemen has been devastated by a war between forces loyal to the internationally-recognised government of President Abdrabbuh Mansour Hadi and those allied to the Houthi rebel movement.
Impoverished Yemen has remained in a state of civil war since 2014, when Houthi rebels overran much of the country, including the capital Sanaa.
The intergovernmental organisation has failed to agree a peace deal to end the fighting, which has left more than 8,600 people dead since the coalition entered the conflict.
A cholera outbreak has claimed more than 2,100 lives in Yemen since April as hospitals struggle to secure supplies amid a coalition air and sea blockade.