A local official and residents said at least six members of General Jaafar Mohammed Saad's entourage also died in the attack, which targeted the governor as he was headed to work. Several other people were wounded.
ISIL, in a statement posted on a messaging service it uses, said it detonated a car laden with explosives aimed at Saad's convoy in Aden's Tawahi district and promised more operations against "the heads of apostasy in Yemen."
A local official and residents said earlier on Sunday a suicide bomber rammed his vehicle into the governor's car.
The group's local branch has stepped up operations since the outbreak of civil war in Yemen, emerging as a forceful rival to al Qaeda in the Arabian Peninsula (AQAP), the main militant group in the country in recent years.
It has launched spectacular attacks on security bases and on mosques run by Houthi forces who control the capital, Sana'a. The Houthis have been fighting a coalition of mainly Persian Gulf Arab forces, which began airstrikes against them in March.