An unmanned aircraft hit a car near Mayfaa, in Shabwa province, near the site of the ambush in which attackers fired a rocket-propelled grenade at an army vehicle, the official said.
The ambush earlier on Monday had left three other soldiers wounded.
The US military operates all drones flying over Yemen in support of Sanaa's campaign against al-Qaeda and has killed dozens of militants in a sharply intensified campaign in the past year.
Drone strikes have triggered criticism from rights activists, who say they have claimed the lives of many innocent civilians.
The United Nations said 16 civilians were killed and at least 10 injured when two separate wedding processions were targeted by drones in early December.
The victims had been mistakenly identified as members of al-Qaeda, the UN quoted local security officials as saying at the time.
Following the deaths, Yemen's parliament voted for a ban on drone strikes, but analysts say lawmakers have limited powers and are unlikely to impact Washington's campaign.
The US says drones are an essential part of its "war on terror".
Yemen is the ancestral home of Osama bin Laden and the home base of al-Qaeda in the Arabian Peninsula, which Washington views as the network's most dangerous franchise.
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