The mass stabbing by the youth, who has been arrested, took place at Russell Square near the British Museum at 10.39 pm local time last night, Scotland Yard said.
Six people were injured in the attack, but a woman believed to be in her 60s who was treated at the scene was pronounced dead later, police said.
However, in the wake of a string of recent attacks in Europe, the authorities said that "terrorism remains one line of inquiry being explored."
"Terrorism is one possibility being explored at this stage," Metropolitan police said in a statement.
"Officers attended the scene along with the London Ambulance Service," the statement said.
Additional police units have been deployed to the area after the attack.
Ambulances and police vans were seen stationed outside Imperial Hotel, near the Russell Square Underground station.
The suspect himself was taken to hospital after being immobilised with a Taser electroshock gun.
London mayor Sadiq Khan urged "calm and vigilance" after knife attack.
The mayor said police were seeking "to establish the full facts including motives" for the attack and urged the city's residents to stay calm but alert.
"I urge all Londoners to remain calm and vigilant... We all have a vital role to play as eyes and ears for our police and security services and in helping to ensure London is protected."
Metropolitan Police chief Sir Bernard Hogan-Howe had warned that a terror attack in the UK was a case of "when, not if."
Since August 2014, the terror threat level in Britain has been "severe" -- the second highest level, meaning an attack is "highly likely".
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