A police officer was also injured in the incident in Ferry Lane in Tottenham Hale on Thursday evening.
The Independent Police Complaints Commission (IPCC) has been called in to investigate the death and it said a firearm had been recovered.
It is thought the officer, who was taken to hospital and later discharged, was shot first but this is not known for certain, an IPCC spokesman said.
In a statement, the IPCC said: "It is understood that the shooting followed an MPS [Metropolitan Police Service] operation."
The Metropolitan Police would not confirm if the man had been shot by a police officer.
A Scotland Yard spokesman added: "One male was pronounced dead at the scene and one officer was taken to hospital."
Local resident David Akinsanya said he arrived at the scene moments after the incident.
He said he was told by a witness that a police officer had shouted to the man to stop "a couple of times", but the man had not heeded the warning.
The witness, who lives next to the spot where it happened, then heard four shots, Mr Akinsanya said.
"There were lots of helicopters and sirens all over the place," he added.
"There was also a surveillance van on the corner."
A waitress at a nearby pub, who did not wish to be identified, said the incident had happened a few minutes' walk from Tottenham Hale station.
She said: "One man came in and he said that he saw police trying to pull some clothes off a man who was bleeding."
Another worker said there were "lots of cars" around the scene.
Police have taped off a large area and Ferry Lane remains closed.
David Lammy, Labour's MP for Tottenham, said he was "shocked and deeply worried" about the attack.
"I think there's quite a lot of anxiety now in the community, but we should try to stay calm and not rush to judgement," he said.
"We need to understand what has happened.
"I hope that the IPCC can move quickly to allay fears and rumours that can circulate in these circumstances."
A man is understood to have been shot dead by a policeman in north London.