The killing took place in the woman's house on Tuesday night.
Locals called police, saying they had heard gunshots from the house. A team rushed there and found the woman's body.
Embakasi police boss John Nyamu said the suspect is known to them and has been on a wanted list.
Detectives are investigating.
“Preliminary findings show it was a love triangle and the man is on our wanted list. We are looking for him and asking him to surrender,” he said.
Elsewhere, two robbery suspects were killed by police in two separate incidents in the city. Two bullets were recovered from them. One was killed in Buruburu area and the other in Kariadudu in Kariobangi during attempted robberies.
Police said the man in Buruburu was wanted for a series of robberies in the area and he was using a green motorbike.
In Kariobangi, the suspect is said to have been with three others and they were terrorising residents who called the police.
Nairobi police boss Augustine Nthumbi said the accomplices escaped on foot. A homemade gun was recovered from the suspect.
Police have increased patrols to prevent armed robberies.
Elsewhere, a woman was arrested in the stabbing death of her husband in Mukarara village, Dagoretti, Nairobi. She had tried to flee.
The woman was identified as Peninah Wanjiru, 33. The victim was identified as George Ogamo, 27.
The weapon was later recovered from the couple's house. Their two children were unharmed.
Police said the woman will be taken for a psychiatric assessment before she is allowed to enter a plea.
Domestic violence and killings are on the rise countrywide, often stemming from depression and suspected infidelity.
(Edited by V. Graham)
