The suspected gunmen opened fire on the checkpoint at the western entrance to the port city of Mukalla, the provincial capital of Hadramawt, the official said.
Two other soldiers were also wounded, the official said.
The assailants stormed a nearby police station where they stripped officers of their weapons, he said.
A military official said AQAP militants established hideouts and training bases in the vast Hadramawt province after the army drove them out of cities in the southern province of Abyan in 2012.
The attack came after Al-Qaeda claimed a brazen assault on last Wednesday on an army headquarters in a highly secure area of Aden, which an official said killed six soldiers and three civilians, in addition to ten assailants and a suicide bomber.
AQAP said the attack killed "nearly 50 soldiers" and was part of its campaign to "target the joint operation rooms that manage the US drones in the country".
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