Al-Qaeda in the Arabian Peninsula (AQAP) confirmed on Twitter it "targeted an army vehicle... heading from Shibam to Seyun in Hadramawt, destroying it and killing the three soldiers on board".
The attack using rocket-propelled grenades took place late on Saturday, the security official said.
Al-Qaeda is active in southern and eastern Yemen, especially in Hadramawt where the authority of the central government is weak.
Signup to our newsletter and follow us on Facebook and Twitter!
AQAP, seen by the United States as the extremist network's deadliest branch, killed 20 soldiers in an attack in Hadramawt last month.
Yemen is a key US ally in the fight against Al-Qaeda, allowing Washington to conduct a longstanding drone war against the group on its territory.
AQAP was born out of a 2009 merger between its franchises in Al-Qaeda founder Osama bin Laden's native Saudi Arabia and his ancestral homeland in Yemen.
The group has exploited instability in the impoverished country since a 2011 uprising forced president Ali Abdullah Saleh to step down.