Officials said at least 60 other troops were wounded in the attack, which occurred near al-Sawlaban military base in Aden's Khor Maksar district, where another Islamic State suicide bomber blew himself up a week ago killing 50 soldiers.
Aden is the temporary capital of Yemen's internationally recognised government in exile in neighbouring Saudi Arabia. It has been battling the armed Iran-aligned Houthi movement since 2014.
Al Qaeda and Islamic State have exploited the war to carry out assassinations and bombings, mostly in lawless southern Yemeni areas nominally controlled by the government.
In a statement posted via its Amaq news agency, IS said Sunday's attacker, who it identified as Abu Hashem al-Radfani, detonated an explosive vest amid a crowd of soldiers.
It posted what it said were pictures of the attack, one showing young man wearing a white vest as he stood next to the black and white Islamic State flag.
The jihadist group put the death toll at more than 70.
Saudi Arabia and its allies in a mostly Gulf Arab military coalition have been bombing the Houthi movement in parts of the country under its control since it drove the government from power in March 2015. They have failed to dislodge the group from the capital, Sanaa.