Daesh (also known as ISIL) said that one of its militants, apparently a Dutch national, carried out the attack on a checkpoint outside the palace in the main city of southern Yemen.
Both soldiers and civilians were among those killed, while at least 17 others were wounded, a medical source said.
A security source said the attack appeared to target the convoy of a local businessman who was entering the presidential complex.
Sources had initially said the convoy was carrying Aden's governor, Aidarus al-Zubaidi, but he later told AFP he was not in the area at the time of the attack.
Zubaidi survived a car bombing earlier this month, after being appointed in December following the murder of his predecessor, Jaafar Saad, in an Aden bombing claimed by Daesh.
Witnesses said the blast damaged at least six vehicles and a nearby mosque.
Former President Abed Rabbo Mansour Hadi was in the palace at the time of the attack but unharmed, a government official said.
Military vehicles from the Saudi-led coalition which supports Hadi were deployed around the complex after the attack, security sources said.