Yemen was previously the preserve of ISIS's terrorist rival Al-Qaeda, which controls swathes of the south and east, but since March the group has claimed a string of high-profile attacks.
The car bomb late Monday targeted a gathering who mourn the death of a family member, a security source said. Eight women were among the dead.
The explosion blew a crater in the road, took chunks out of nearby walls and left debris strewn across the street.
In a statement posted online, ISIS said it had organised the attack on what it called a "Shiite nest".
Just Friday, a Saudi ISIS suicide bomber killed 26 people and wounded 227 in a Shiite mosque in Kuwait.
In Yemen, ISIS claimed a car bombing that killed two people outside a Shiite mosque in Sanaa on June 20 and a series of attacks in the capital four days earlier that killed 31.