The assassination attempt on Governor Aidarous al-Zubaidi comes a month after his predecessor was killed in a bombing claimed by a local Islamic State affiliate.
Al-Zubaidi has been cracking down on extremist groups, which have exploited the chaos of Yemen's civil war. Last week, government forces retook the strategic Red Sea port from several militias.
The officials said the blast was heard throughout Aden. They spoke on condition of anonymity in line with regulations.
A Saudi-led coalition has been carrying out airstrikes and fighting alongside government forces.
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Pro-government forces drove the Houthis out of Aden in July last year, which was seen as a major morale boost for anti-Houthi forces.
The government has returned to Aden from Saudi Arabia, but has been struggling to control the city as al-Qaida and other militant groups have moved in.