A local official and residents said earlier on Sunday a suicide bomber rammed his vehicle into the governor's car.
Islamic State'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.
Spectacular attacks have been launched on security bases and on mosques run by Houthi forces who control the capital, Sanaa. The Houthis, who follow the Zaydi branch of Shi'ite Islam, have been fighting a coalition of mainly Gulf Arab forces, which began air strikes against them in March.