Sheikh Abdulrahman al-Adani was shot dead as he was heading to a mosque near his home, the official said.
Adani headed a Salafist religious school which attracts both local and foreign students.
He was known for his stance against the Shiite Huthi rebels as well as against the Islamic State group and Al-Qaeda which are becoming increasingly active in Aden, sources there said.
According to Zaid al-Sallami, an Aden-based expert on Islamist groups, Adani was known for "rejecting violence and terrorism".
Al-Qaeda and IS have stepped up attacks in Aden despite the efforts of the government and its backers in a Saudi-led coalition battling the Huthis and their allies to secure it.
In another sign of growing unrest in Aden, clashes broke out near the entrance to the presidential palace in the port city's Crater district between presidential guards and soldiers demanding their salaries, an official told AFP.
The fighting spread to nearby residential districts and there were casualties, the official and residents said.
President Abedrabbo Mansour Hadi's internationally recognised government has declared Aden the country's provisional capital after the Huthis and their allies drove it out of Sanaa and much of northern Yemen since September 2014.
Because of the unrest gripping Aden, Hadi himself and many senior officials in his government spend most of their time in Riyadh, which has led an anti-rebel coalition since March 26 last year.
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