The dawn strike targeted their car as it left the base of the 27th Mechanised Brigade in the Hadramawt provincial capital Mukalla, the official told AFP.
Fighters from the Sunni extremist group seized the camp from forces loyal to President Abedrabbo Mansour Hadi in April, consolidating their grip on Mukalla.
They have exploited months of fighting between Hadi loyalists and Iran-backed Shiite Huthi rebels to consolidate their grip on Yemen's southeast.
The official identified the victims as Shuaib al-Maliki of Saudi Arabia and the Kuwaiti Abdul Aziz al-Otaibi, along with two Yemenis.
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The group confirmed on June 16 the killing by an American drone strike of Nasir al-Wuhayshi, who headed Al-Qaeda's Yemen branch.
Washington regards that branch, known as Al-Qaeda in the Arabian Peninsula (AQAP), as its most dangerous and has kept up a drone war despite the pullout of US troops from Yemen in March as the country's war worsened.
The US still has drones and other aircraft at bases in Saudi Arabia and Djibouti.
Since the war in Yemen worsened in March and a Saudi-led coalition began bombing the Shiite Huthi rebels, jihadists from the Islamic State Sunni extremist group have also taken advantage of the chaos.
They have claimed a series of attacks including a car bomb in Yemen's capital Sanaa which killed at least 28 people on Monday.