Mohammed Abdi Ali, Nuseiba Mohammed Haji and Fatuma Mohammed Hanshi have been arrested
Kenyan police say they have foiled a "large-scale" biological attack using anthrax, by a terror group with links to so-called Islamic State (IS).
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".
The statement says Mr Ali's network included medical experts who could help organise a biological attack using anthrax.
His wife, Nuseiba Mohammed Haji, a student, was also arrested, in Uganda, as was a friend, Fatuma Mohammed Hanshi.
The police said accomplices of Mr Ali had gone in to hiding, including Ahmed Hish and Farah Dagane, who are medical interns.
Police described them as "armed and dangerous" and offered two million Kenyan shillings (£14,000; $20,000) for information leading to their apprehension.
The statement from Kenya's police chief Joseph Boinnet described the arrests as being linked to "a terror plot by an East African terror group network that has links to Isil (Islamic State)".
But there is no detail as to the group's name, nor evidence for its affiliation to IS.
A group calling itself Jahba East Africa has recently emerged and pledged allegiance to IS, but it is not known if they are connected to the "foiled terror plot", as police described it.
There is a split within the Somalia-based militant Islamist group al-Shabab over allegiance to either al-Qaeda or IS.
While there are thought to be some IS-linked militants fighting in Somalia, Emmanuel Kisiangani from the Institute for Security Studies in Nairobi believes it is unlikely they would target Kenya.
"I cannot discount the idea they would be recruiting for Syria, but in targeting Kenya I don't see any connection, even remotely," he said.
Mustafa Ali, an expert in conflict resolution and violent extremism in Kenya, said an anthrax attack in Kenya was "less likely, but then it was less likely the US would be attacked in that way in 2001", referring to a series of attacks that left five people dead.
He said the aim of IS is to create terror anywhere they are able to carry out attacks.