The 27-year-old allegedly strangled them using a robe and left the bodies on the floor of his house in Lelaitich village. The children were aged nine, six and three.
The man is said to have fought with his wife over his extramarital affairs and she left for her parents' home a week ago.
"Both have always engaged in bitter arguments to an extent of fighting, something that forced the wife to flee their matrimonial home," Cecilia Maritim, a neighbour, said.
“They might have had marriage issues because the husband always stays with the children. I had asked him why he committed the atrocious act and he told me the wife returned home recently with a newborn after some time away. He said he did not know who fathered the baby.”
Chief Robison Rotich said it was unclear why the man killed his children, adding that it could be because of marital disputes.
“From the reports we have so far gathered from close family members, the suspect had on Thursday morning followed the wife to her Transmara home in the neighbouring Narok county, to request her to return home.”
A family member who requested anonymity said the children had supper with their grandmother in her house that evening before leaving to for their home a few metres away.
Their grandmother woke up early the next day and prepared their breakfast. She, however, grew impatient because they were taking too long and went to check on them.
That's when she found the bodies and called for help. Their father was nowhere to be found.
“With the help of the members of the public we mounted a search of the suspect and managed to arrest him some 5 kilometres from their home,” Rotich said.
The suspect was taken to Chebunyo police station.