The naked body of an unidentified pregnant woman was on Tuesday morning found by the roadside in Mwiki.
The body of the woman, who police say was seven months pregnant, had injuries.
Police moved the body to City Mortuary as they launched investigations to establish who is behind the murder.
Meanwhile, three suspected thugs were gunned down by police officers in two separate incidents on Monday and at the weekend.
In one incident, two suspects were shot dead by plainclothes police officers in Masimba area, Kayole while the other one was shot dead in Buruburu.
The Kayole incident happened after members of the public alerted the police that a group of young men was causing panic in the area.
The slain suspects were found in possession of a homemade gun.
Police have said they are in pursuit of three other suspects who managed to escape the Kayole shootout.
The incident comes at a time when Nairobi police boss Philip Ndolo has warned criminals that they will not be spared in the fight against crime.