The car bomb targeted Huthi rebel chief brothers Faycal and Hamid Jayache last night during a gathering to mourn the death of a family member, a security source said.
Huthi rebels closed down the surrounding area in the centre of the city after the attack, only allowing through emergency services to help evacuate the victims, witnesses said.
The explosion blew a crater in the road, took chunks out of nearby walls and left debris strewn across the street.
The extremist Sunni jihadist group considers Shiites as heretics and has frequently targeted them in attacks in several countries.
The latest of these, a suicide bombing by a Saudi national on Friday in a Shiite mosque in Kuwait killed 26 people and wounded 227 others.
IS has also claimed a car bombing on June 20 against a Shiite mosque in Sanaa that killed two and wounded 16 and another series of attacks in the Yemeni capital four days earlier that killed 31.
Iran-backed Huthi rebels have seized vast swathes of the country since launching an offensive in July 2014, forcing President Abedrabbo Mansour Hadi to flee to Saudi Arabia.
Neither peace talks in Geneva nor a Saudi-led air campaign begun in March have driven them from power and they remain locked in battle with pro-government fighters, Sunni tribesmen and southern separatists.
Yemen's official Saba news agency, which is controlled by the Huthis, reported early today that the rebels had launched a scud missile at the Al Salil military base, near the Saudi capital Riyadh.
"This is another message to the forces of oppression," he added, promising "new surprises in the coming days."
Saudi Arabia did not immediately confirm or deny the missile attack.
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