Sheik Aboud Rogo Mohammed died Monday in a drive-by shooting, the Kenya Broadcasting Corp. reported.
Businesses were shuttered downtown by rioting that erupted Tuesday in various parts of the city. Additional anti-riot police were brought in after protesters threatened to burn down churches.
Three persons have been reported injured in the violence.
The U.N. Security Council had accused Rogo of being the "main ideological leader" of al-Hijra, a Kenyan group seen as an ally of Somalia's al-Shabaab extremists.
The Security Council imposed a travel ban on Rogo in July and froze his assets.
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