The militants attacked the building from two sides, firing rocket-propelled grenades and automatic weapons inside.
The “well-planned” attack took place in Aden’s coastal Tawahi neighborhood.
Al-Qaeda remains active in the area, after a security vacuum was created in a year of protests against former president Ali Abdullah Saleh.
Militants have seized large parts of the south and east of the country.
A recent, two-month military offensive backed by the US drove them from their strongholds in towns in the southern Abyan province but many escaped into nearby mountains from where they continue to launch attacks.
Among the dead in the Aden attack were at least 11 soldiers, many of whom were reported to be sleeping when hand grenades were thrown into their rooms.
The militants launched the attack from both sides of the intelligence complex, situated next to a state television building. They then managed to escape.
“The operation seemed to have been well planned,” a security source told Reuters, adding he believed the attackers belonged to Al-Qaeda.
A few weeks ago, suspected Al-Qaeda militants carried out a suicide bombing that killed at least 45 people during a funeral in the city of Jaar.
In May, more than 90 people died in a suicide bomb attack at a military parade rehearsal in the capital, Sanaa.
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