Muslim youths have been battling police since Rogo was murdered by unidentified gunmen on Monday in an attack that left his wife and child unhurt.
Raila Odinga, the nation’s prime minister has called for calm.
"Let's act with restraint as law enforcement agencies get to the root of the matter," he said.
"We urge Muslims and Christians not to fight."
Rogo was a supporter of al-Shabaab, the Islamic militant group that controls large swathes of neighboring Somalia.
The U.S. government suspected him of serving as al-Shabaab’s principal chief in Kenya, where he reportedly found recruits to fight the government in Somalia.
Kenyan authorities believed he was arranging to transfer funds to the organization, which has been linked to al Qaeda.
In July, the United Nations Security Council imposed sanctions on Rogo and prevented him from leaving Kenya.
Mombasa is a Muslim-majority city, but Islam is a minority faith in Kenya, which is overwhelmingly Christian.