The cleric, Sheikh Ibrahim Ismail, was seen as the successor to Aboud Rogo Mohammed, a radical preacher who was gunned down in August last year, sparking unrest in Mombasa, including attacks on churches.
Rogo was on US and UN sanctions lists for his alleged links to the Somali militant group al-Shabaab and al-Qaeda.
The Nation newspaper quoted police as saying Ismail and four others were traveling in a car from mosque on Thursday evening when the incident took place. Only one passenger survived the attack.
Al-Shabaab claimed last month’s attack on the Westgate shopping centre, which left at least 72 people dead, including 61 civilians, six soldiers and five assailants.
Investigations into the attack are ongoing. – dpa