The State Department issued the order on Wednesday as the Houthi movement, which is aligned with Iran, has stepped up hostilities against Saudi Arabia.
"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," State Department spokesperson Tommy Pigott said in a social media post.
"The safety and security of Department personnel and their families remain our highest priority, and we will continue to take all necessary steps to protect and support them," he added.
Pigott said an earlier media report about US plans for the departure of some personnel and family members at embassies across the Gulf was "inaccurate." However, four US officials told the Reuters news agency that US missions in other Gulf states would also be ordering family members to leave.
The US embassy in Riyadh issued a security alert on Wednesday warning of possible further Houthi attacks on Saudi Arabia after recent deadly strikes, including on Riyadh's airport. The embassy and a CIA station hosted there came under drone attack in early March, as Iran began launching attacks across the region.
The United States had returned some diplomatic personnel to the region in recent months after many were pulled out when Tehran launched attacks on US facilities following the start of the US-Israeli war on Iran in late February.
The withdrawals follow an escalation of fighting in Yemen, opening another front in the regional conflict triggered by the war. The conflict has snarled global energy trade and hurt Gulf economies.