A Pakistani national was killed in the attack late on Sunday and at least 11 others were injured, the Saudi civil aviation authority said in a statement on X early on Monday.
The attack caused property damage, the extent of which was being assessed, the authority said.
It was the second attack on the airport in as many days, with at least 13 killed and more than 300 others injured in a Saturday attack.
The aviation authority also reported an attack on King Fahd Airport in Dammam on Sunday that had caused damage.
Yemen's Houthis claimed responsibility for the attacks and warned that the kingdom's airports and airspace were "legitimate targets" for the Iran-aligned militia - with the exception of Mecca and Medina, which are sites sacred to Muslims.
The Houthis said they had carried out four attacks in Saudi Arabia in the previous 24 hours - using ballistic missiles, cruise missiles and drones.
The targets included the two airports, a gas plant and an oil refinery belonging to the state-owned oil company Aramco, according to their report.
The Houthis said Saudi Arabia carried out 124 air strikes in Yemen in the past 24 hours, including against the capital Sanaa and the group's stronghold Saada.
Yemen's Houthi-run foreign ministry said that further Saudi military action in Yemen would trigger a stronger response, adding that its actions would be guided by the principle of reciprocity.
"Unless the Saudi enemy stops its aggression and interference in Yemen, worse is yet to come, God willing," the ministry said in statements carried by Houthi-run Al Masirah television.
The allied states of the so-called R4 Group - Turkey, Egypt, Pakistan and the Kingdom of Saudi Arabia - jointly condemned the attacks by the Houthi militia as a "flagrant violation of the Kingdom's sovereignty and territorial integrity".
In a statement, the group spoke of "a direct threat to its security, stability, and the safety of civilians, and it is a dangerous escalation that cannot be justified or accepted under any pretext".
The Houthis have been fighting Yemen's internationally recognised government for more than a decade. A truce reached in 2022 largely froze the conflict but failed to pave the way for a lasting peace.
Flight-tracking website Flightradar24 showed several delays and cancellations on Sunday evening for arrivals and departures at Dammam airport, which serves the capital of the oil-producing region and is the kingdom's third-largest airport.
Fighting has recently flared up again against the backdrop of the wider war involving Iran, further deepening Yemen's humanitarian crisis.
US President Donald Trump said the US was considering joining Saudi strikes on the Houthis in the conflict, a spillover from the wider war with Iran that the US and Israel launched in February.
Saudi authorities notified parents that in-person classes at all schools in Riyadh would be suspended and shifted to remote learning from Sunday until Thursday.
Saudi Arabia, one of the world's largest oil producers, has previously blamed the Houthis for attacks on civilian facilities in the kingdom and launched retaliatory strikes against rebel targets in Yemen.
with Reuters
5°C