Security forces began the operation in the early hours of today morning, targeting the Masjid Musa and Sakina mosques in Mombasa.
"We had information that the group has been planning an attack, and that is why the raid was conducted," Mombasa police chief Geoffrey Mayek said.
"We have arrested several of them, including six notorious ones," he added.
Police said one man was killed but gave no details as to how he died, with the operation still ongoing.
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Western nations have warned their nationals to avoid all but essential travel to Mombasa, a key transport hub as well as important tourist hub for the country's Indian Ocean coastline.
The city has been hit by bombings and shootings since Kenya invaded Somalia in 2011 to attack the Shebab, later joining an African Union force battling the Islamists.
The Shebab carried out the September 2013 attack on Nairobi's Westgate shopping mall, killing at least 67 people as a warning to Kenya to pull its troops out of southern Somalia.