The claim came in a short statement posted on Twitter by the group's semi-official Amaq news agency.
The agency, affiliated with the IS, claimed that the attack conducted by a jihadist fighter killed about 60 new recruits.
Medical sources in Aden told Xinhua the death toll has risen to about 65 and that more than 80 others were injured in the attack.
Earlier in the day, the medical charity Medicins Sans Frontieres said on Twitter that its hospital in Aden received 45 dead and at least 60 wounded from suicide blast.
Aden-based security sources said that a suicide bomber slammed his explosives-laden car into a gathering of army recruits near a school in Aden's Mansourah neighborhood.