The people were arrested in Rachuonyo East, Homa Bay County, on Sunday as suspects in a murder and robbery incident.
The victim, 32-year-old Okeyo Obange, was attacked at his house in Ang’eny village, Kojwach, on Saturday night when he returned with Sh9,000 after selling his cow at the local market.
Chief James Oindi said the three were among people who attacked Mr Obange and stole his money after he sold the first cow two weeks ago.
"He reported that some youths wanted to steal from him after he sold the cow two weeks ago. He named people whom he accused of breaking into his house and attempting to steal his money," the chief said.
He said other suspects were in hiding.
Mr Oindi said the man had visible injuries on various parts of the body.
“The man had injuries that indicated he had been beaten and strangled," the administrator said.
He warned youths against engaging in crime, saying security agencies would take action against them.
Sub-county Police Commander Charles Barasa said the suspects were taken to Oyugis Police Station amid a search for their accomplices.
“We expect the suspects to give us more information about the death and their accomplices before they are arraigned. We will not relent until the remaining suspects are arrested."
The body was taken to Rachuonyo Sub-county Hospital Mortuary in Oyugis town.