The violence has led to the death of at least one person and the looting of two churches in the coastal town.
Aboud Rogo Mohammed died instantly in the attack, while his wife and two children were wounded.
"There is absolute chaos in the city at the moment," said Geoffrey Njuguna, security manager at a Mombasa hotel, according to the Daily Telegraph.
Aggrey Adoli, a local police commander, told the Telegraph that more than 2000 young men with weapons and machetes rioted in the streets before police could restore some sense of order in the popular resort. Many businesses were shut down during the disturbances.
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.
The UN accused him of providing "financial, material, logistical or technical support to al-Shabaab". He was also suspected of having plotted attacks in Mombasa himself.
In 2005, Rogo was cleared of charges that he that had masterminded a 2002 attack on a local hotel which killed 12 people, including tourists from Israel.
Islam is a minority faith in Kenya, which is overwhelmingly Christian. According to the CIA World Factbook, only about 10 percent of the population are Muslim, while almost 80 percent practice some form of Christianity.
Over the past year, the Kenyan military, in tandem with the forces of the Somalian government, have conducted raids into Somali territory to catch al-Shabaab militants who had captured Western tourists.
Kenya is particularly concerned about Islamic militancy in the country since the bombings by al-Qaeda at the U.S. embassy in Nairobi in the summer of 1998 killed more than 200 people.