Sheikh Ibrahim Omar's death ignited religious tensions in the commercial and tourism hub in east Africa's largest economy, two weeks after Islamist militants killed at least 67 people in a raid on Nairobi's Westgate shopping mall.
The imam was shot dead in Mombasa on Thursday night, police said. He preached at a mosque that has in the past been linked to the Somali al Shabaab Islamists who claimed responsibility for the shopping centre attack. He was found dead in a car hit by more than a dozen bullets, television images showed.
Youths torched a Salvation Army church and temporarily blocked the main road into the city, a witness said.
Kenyan police in riot gear fired gunshots and tear gas to break up the crowd.
The worst of the running battles with police took place in Mombasa's downtrodden Saba Saba neighbourhood, where traders shuttered their shops and residents fled for safety.
"We are trying to deal with some youths who have started bringing trouble within town," police said. "They are few. We will contain them."
The imam was shot in Mombasa's outskirts on the main road to the resort town of Malindi, a few hundred yards from where another firebrand cleric, Aboud Rogo, was shot dead in his vehicle in August 2012 in a strikingly similar attack.
Kenya had accused Mr Rogo of recruiting and fund-raising for Somalia's al Shabaab militants. His death last year unleashed riots in Mombasa's run-down neighbourhoods, where he commanded a support base.