Police fired an electric stun gun in arresting the 19-year-old man and said that while they were focusing their inquiry on his mental health, counter-terrorism officers were supporting the murder probe.
With European cities already wary of attacks, London Mayor Sadiq Khan appealed for calm and vigilance, while extra police have been deployed in the British capital, including armed officers – an unusual sight in the UK.
After receiving hospital treatment himself, the suspect was being held at a south London police station.
The attack took place early this morning in Russell Square, a plush garden square lined with tourist hotels close to several popular attractions, notably the British Museum.
Paramedics fought to save the life of a woman believed to be in her 60s but she was pronounced dead at the scene.
Two women and three men were also injured. Two of the five remain in hospital while three have been discharged.
“Early indications suggest that mental health was a factor in this horrific attack. However, we are keeping an open mind regarding the motive,” said London police’s counter-terror chief Mark Rowley.
Extra armed and unarmed officers were being deployed on the streets in a bid to reassure the public following recent events abroad, police said.
Police were alerted to the incident at around 10:30pm (4:30am Thai time). Armed officers were on the scene within around five minutes and the man was detained at 10:39pm (4:39am Thai time).
“I was buying a beer when I heard a woman shouting who was being chased by a man,” said Xavery Richert, 22, a French tourist staying in a youth hostel on the square.
“I thought it was a bag snatching... she was not hurt,” he said.
“I came out for a cigarette, I went back, there were firefighters, police, and then I saw the body under a sheet. You could only see the feet sticking out.”
Russell Square resident Constantine Somerville said: “It’s such a safe area and very quiet especially at night – why would somebody commit an attack in such a quiet area?”
Mayor Khan 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.”
Europe has been on edge for months following a string of recent jihadist-inspired attacks.
Since Aug 2014, the terror threat level in Britain has been “severe” – the second highest level, meaning an attack is considered “highly likely”.
Writing in The Mail on Sunday newspaper, Britain’s top police chief Bernard Hogan-Howe said a terror attack was a question of “when, not if”.
Hours before the stabbings, police announced that the first of an additional 600 armed officers were trained and ready to hit the streets.
While British police officers are not routinely armed, those that are carry handguns and semi-automatic weapons, as well as electric stun guns.
Following the Paris attacks last year, Hogan-Howe decided to increase the number of armed police in London from the existing 2,200.
Armed patrols are already in place outside major London locations such as the Houses of Parliament.
This morning’s stabbings came two days after a mentally unwell man was jailed for life for a knife attack at a London Underground station.
Paranoid schizophrenic Muhaydin Mire, 30, tried to behead a commuter in December in an Islamic State-inspired attack. The Somali-born man also swiped at other passers-by.
And in May 2013, two British Muslim converts killed soldier Lee Rigby in broad daylight, using blades.