A Christian church in the Mombasa suburb of Majengo was set on fire during the violence, The (Nairobi) Standard reported.
Hundreds of armed police have been deployed in Islamist strongholds around the region in anticipation of more violence after Friday afternoon prayers.
Sheik Ibrahim Rogo was killed in a drive-by shooting on a highway shortly after he delivered a lecture at a mosque in Majengo, police said. Three men in Rogo's vehicle also were killed.
A fourth person in the vehicle received minor injuries.
Sheik Abubakar Shariff, an Islamist militant, declared the killings an "assassination." He said Muslims were justified in disobeying Kenyan law "because we cannot sit back and be slaughtered or see our sheiks killed everyday."
Controversial cleric Sheikh Aboud Rogo Mohamed was killed along the same highway last year, The (Nairobi) Star reported.