Additionally, authorities extended the closure of Riyadh's international airport until Saturday to "allow for the completion of procedures to ensure the safety of the airport."
The Iran-backed Houthis threatened on Monday to launch a "swift and painful response" against the US and its regional interests if Washington joined Saudi Arabia's military campaign in Yemen, Houthi political bureau member Mohammed al-Bukhaiti told AFP.
"If the US becomes involved in the aggression against Yemen, we will not deliberate over the decision to respond; rather, there will be a swift and painful response targeting the US and all its interests in the region," Bukhaiti said.
His warning came following US President Donald Trump’s comments weighing American involvement following the recent deadly attacks on Saudi infrastructure, including a strike on King Khalid International Airport in Riyadh on Saturday that killed 13 people and wounded hundreds more. The attack was the deadliest on Saudi soil in more than a decade.
Trump said the airport attack was "not acceptable" and indicated that Washington was considering joining Saudi strikes against the Houthis, after reportedly rejecting earlier requests for military assistance from Riyadh.
"The Houthis are misbehaving very badly. They're misbehaving very badly. No good," Trump said on Monday.
Bukhaiti warned, "all employees and workers at Saudi oil facilities and airports to stay away from these sites, as they have become legitimate targets."
He said the Houthi campaign was intended to demonstrate to the crown prince "that he can no longer wage aggression against Yemen from a safe position".
Saudi capital's airport to remain shut this week as airlines cancel services
Authorities also extended the closure of Riyadh's international airport until Saturday and suspended operations at King Khalid International Airport 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.
Late on Monday, the Houthis said they had attacked the airport with a ballistic missile, shortly after Saudi Arabia said it had intercepted and destroyed a ballistic missile fired by the group towards Riyadh.
The Houthis also said in a statement that they targeted an airbase in Khamis Mushait in the kingdom's southwest with a drone. There was no immediate Saudi confirmation.
A Notice to Airmen issued on Monday showed King Khalid International Airport will stay closed until October 17.
The attacks have also raised worries over civil aviation becoming a target in armed conflict.
"This level of sustained intense attack on civil aviation is unprecedented," said Mark Zee, founder of OPSGROUP, a membership-based organization that provides aviation safety advice.
"I think this requires us to rethink how we view the current risk picture, and tread very carefully," he said.
Air traffic tracker Flightradar24 showed planes avoiding the city on Monday, though jets crossed Saudi airspace and landed at the country's top hub, Jeddah, on the west coast.
Cancellations across all Saudi airports reached 46.4%, Cirium, an aviation analytics firm, said.