"The man chopped off the head of a young child using a panga (machete), tapped and sucked blood and then drank it, before starting to eat part of the head," Rift Valley deputy police chief Peter Leiyan said on Tuesday from the regional capital, Nakuru.
"Police were alerted by the wailing mother and neighbours and we arrested the suspect while he was boiling the head to drink the soup as well as eat it," Peter added.
The incident happened at a village in Koibatek district on Saturday.
The man's motives were being investigated, said police, adding that he had no known history of cannibalism.
Koibatek Police chief, Maurice Kiplagat, said the suspect attacked the one-year-old boy after fruitless attempts to send his mother back to her estranged husband.
"They quarrelled and the suspect stormed into his father's house, armed himself with a machete and chopped off the boy's head," Kiplagat told the Tuesday edition of the east African Standard newspaper.
Immediately after the incident, the aggrieved mother ran away screaming, neighbours responded swiftly and found the man quietly seated in the kitchen waiting for the soup to boil, the Standard said in a front-page story.