A security official told Reuters news agency that the suicide bomber detonated his explosives on Saturday as troops were waiting to collect their salaries at the entrance to the Sawlaban base on the outskirts of Aden.
The official said another 70 people were wounded in the attack.
ISIL claimed responsibility for the attack, according to Amaq, a news agency that supports the group also known as ISIS.
However, Aden al-Ghad, a local news website, said the men were not soldiers but young men registering to take part in an offensive to break the siege of Yemen's second largest city, Taiz.
The port city has seen a wave of bombings and shootings targeting officials and security forces.