The officials said the bomber targeted young men queuing to enlist, at the home of a senior army commander in the Khormaksar district.
The Islamic State of Iraq and the Levant (ISIL, also known as ISIS Daesh) claimed responsibility for the two attacks, which were carried out on Monday, Al Jazeera reported.
Yemen’s Saudi-backed former President Abd Rabbuh Mansur Hadi is based in Aden.
Local news website Aden al-Ghad showed pictures of soldiers picking up bloodied comrades in uniform from the ground and witnesses reported seeing ambulances with blaring sirens collecting the wounded from the scene.