About 100 troops, including Special Forces commandos, are leaving the base near the southern city of al-Houta, the officials said.
Al-Houta was stormed by al-Qaeda fighters on March 20, although they were later driven out by the Yemeni army.
The US military has not confirmed the evacuation.
It comes a day after suicide bombers killed at least 137 people in the capital Sanaa. Militants allied to Islamic State (ISIS) said they carried out the attack.
There are mounting tensions between various powerful, armed elements in Yemen, including Houthi rebels, al-Qaeda and ISIS.
US troops at al-Anad air base have been training Yemeni fighters to launch attacks against al-Qaeda operatives.
On March 20, al-Qaeda fighters took control of al-Houta, near to the airbase. But the militants were later driven back by the army.
The US closed its embassy in Sanaa in February after Houthi rebel forces took over the city.
Yemen is the base of al-Qaeda in the Arabian Peninsula (AQAP), a powerful offshoot of the jihadist militant group.
ISIS is also gaining ground in Yemen, after setting up a base in the country in November.
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