According to the police on Monday, the 33-year-old man was arrested on Sunday evening while watching the European Championship final in a pub, investigators said.
The police said the man has admitted murdering 42 women.
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He then dismembered them and put their remains in plastic bags before throwing them into a former quarry in a Nairobi neighbourhood.
“We are dealing with a psychopath, a serial killer with no respect for human life,” said Mohamed Amin, the head of the criminal investigation department.
The investigation began last Friday after body parts were found at the dump.
By Sunday, the police had found the remains of nine women aged between 18 and 30.
The arrested man claimed that his first victim was his own wife, said Amin.
He had strangled and dismembered her, and went on to do the same to the other women.
Investigators tracked the man down via the mobile phone of his last victim.
He reportedly lived just 100 metres away from the dump.
In addition to a machete and plastic bags, personal belongings of his alleged victims were also found in his house.
At the time of his arrest, the man was reportedly already looking for his next victim.
Acting Inspector General of Police Douglas Kanja said the 33-year-old prime suspect had been arrested at about 3am local time (00:00 GMT) near a bar in a joint operation by the Directorate of Criminal Investigations and the National Police Service.
He said a total of nine bodies had now been recovered so far and that autopsies on the victims would be carried out on Monday.
A video posted on social media also showed police presenting several pieces of evidence reportedly linked to the suspected killer.
Since Friday, mutilated and dismembered bodies – trussed in plastic bags – have been pulled from the rubbish heap in the Mukuru slums in the south of the capital, horrifying the country
