The attack wounded and killed "members of the Security Belt... in an explosion of a motorbike-borne device in the Saad area of Aden," IS said via its propaganda arm Amaq, referring to a UAE-backed force of southern separatists who control the city.
It marks the first attack of its kind in Aden since Yemeni government forces were expelled from the city on August 10.
A security source earlier told AFP "a suicide bomber crashed his bomb-laden motorbike into a vehicle of the Southern Transitional Council on a roundabout in the Sheikh Saad district" of northern Aden.
Three of those on board the vehicle were killed and an unknown number wounded, including civilians near a busy marketplace, the source said.
A security official had initially blamed the suicide bombing on Al-Qaeda.
In a separate attack, the military head of the Security Belt force survived a roadside bomb attack on his convoy in central Aden that wounded five of his guards, security sources said.
The Security Belt force, dominated by the separatist Southern Transitional Council, once again seized control of Aden, Yemen's interim capital, on Thursday after clashes with government forces who had re-entered the city just hours before.
On August 1 separate attacks by jihadists and Huthi rebels killed dozens of separatist fighters and the separatists accused the government of complicity.