"The US Department of State issued an ordered departure for non-emergency US government employees and their family members in Saudi Arabia," a state department spokesperson said in a statement.
"Iranian-supported Houthis have increasingly engaged in hostilities against Saudi Arabia, including attacks on civilian airports and other critical infrastructure resulting in civilian casualties and severe travel disruptions," it added.
The spokesperson also warned "the hostilities have the potential to escalate rapidly".
In the latest attack on the King Fahd International Airport eight people sustained injuries that ranged from "minor to serious", officials said.
No details of the attack have yet been given, but the strike comes after airports in Saudi Arabia have been repeatedly targeted by Houthi forces.
The energy ministry has also not said who had launched the drone aimed at the Shaybah oil field near the border with the United Arab Emirates that left two people injured.
Yemen has been devastated by a civil war that began when the Houthis ousted the government from the capital, Sanaa, in 2014. Conflicts escalated in 2015, after a Saudi-led military coalition tried to restore the government's rule.
An informal ceasefire had been in place for the past four years, but it unravelled in July after the Houthis announced a "maritime embargo" against Saudi Arabia and began missile and drone attacks on Saudi airports, oil facilities and tankers in the Red Sea.
The Houthis said they were retaliating for what they have called a Saudi blockade of their territory, as well as an air strike on Sanaa airport that they blamed on the kingdom.
The group's "maritime embargo" in the Bab al-Mandab Strait along Yemen's south-western coast has contributed to a surge in global oil prices because Saudi Arabia had been relying on the Red Sea for oil exports since the US and Israel's war with Iran effectively closed the Strait of Hormuz in the Gulf.