Saudi Arabia earlier issued a warning alert for a potential "hostile threat" in Riyadh.
The Houthi rebels have been attacking Saudi airports and oil facilities since last week as part of a rapidly escalating conflict.
State-run media in Saudi Arabia said the country's forces responded to attacks from Houthi rebels but did not give further details.
Air strikes on Yemen's capital Sanaa killed one person and wounded 12 others, according to the Houthi-run health ministry.
Ministry spokesman Anees al-Asbahi said a strike on a salt factory in Sanaa's Hamadan district killed a man and wounded eight people.
A separate strike on a house wounded a woman and three children, he said.
The rebels' media centre blamed Saudi Arabia for the strikes, which came as the Houthi militia continued to fire missiles and drones toward the kingdom's airports.
Operations at King Khalid International Airport, Saudi Arabia's second-busiest airport after Jeddah, were suspended to "allow for the completion of procedures to ensure the safety and operational readiness of the airport's facilities," the Saudi civil aviation authority said in a statement.
The airport has been shut since an attack on Saturday that killed 13 people and wounded more than 300, the deadliest in the kingdom in more than a decade.
On Sunday, another attack killed one person and injured nearly a dozen others.
The attacks marked one of the most significant disruptions to Saudi aviation in years, adding to pressures on an industry already grappling with conflict across the Middle East and with higher jet fuel prices that are eating into profits.
The airport cancelled 82 per cent of all scheduled flights on Monday, according to aviation analytics firm Cirium, which said the final number may be higher.
Cancellations across all Saudi airports reached 46.4 per cent, Cirium said.
An air traffic tracker from Flightradar24 showed planes avoiding the city on Monday although jets were crossing Saudi airspace and landing at top hub Jeddah on the country's west coast.
with Reuters
