A man, his wife and another woman have been arrested. Rewards have been offered for two other men.
Police did not name the network, but said it stretches across the country and outside its borders, including to Somalia, Libya and Syria.
In a statement, the police said Mohammed Abdi Ali, a medical intern at a Kenyan hospital, was in charge of a “terror network… planning large-scale attacks akin to the Westgate Mall attack” in which 67 people were killed.
They say he was also “engaged in the active radicalisation” of students and helped recruit Kenyans “to join terror groups in Libya and Syria”.