Emergency services were called to a property in Nightingale Road, Edmonton, just after 1pm on Thursday to reports of a man with a machete.
Armed officers responded and discovered the woman in a garden.
She was pronounced dead at the scene.
Police said there is no suggestion that the killing had any terrorist motives.
A 25-year-old man has been arrested on suspicion of murder and remains in custody.
The man is in hospital being treated for injuries suffered when he was arrested, police said.
One firearms officer was injured during the course of the arrest and is believed to be suffering from a broken wrist.
A taser was discharged by officers.
DCI John Sandlin, who is leading this investigation, said: “This is was a highly visible attack in broad daylight on a residential street. I can understand why this may cause people concern, however we are confident that we are not looking for anyone else at this stage.
“Whilst it is too early to speculate on what the motive behind this attack was I am confident, based on the information currently available to me that it is not terrorist related.”
Resident of the area, Muhammed Yusuf, said police knocked on his door and told him to leave the property immediately.
He said: “They just said ‘You’ve got to get out of the house’. Of course I was worried.”
His son Ahmed, 19, said: “At first there were two police cars, then all of a sudden there were 20.
“The police said to drop everything. I said ‘What’s going on?’ and they said there’s a guy jumping over gardens.”
London Ambulance Service said they sent a number of resources to the scene including London’s Air Ambulance, an ambulance crew and a duty manager.
The case is being investigated by Scotland Yard’s Homicide Command and the police watchdog, the Independent Police Complaints Commission, has also been informed of the incident.