Armed police were called at 10:33 p.m. (2133 GMT) after a man with a knife started to attack people in London's Russell Square, an elegant park near the site of a 2005 suicide bombing.
"Early indications suggest that mental health is a significant factor in this case and that is one major line of inquiry," London Metropolitan Police Assistant Commissioner Mark Rowley told reporters.
"But of course at this stage we should keep an open mind regarding motive and consequently terrorism as a motivation remains but one line of inquiry for us to explore," said Rowley, who is Britain's most senior anti-terrorism officer.
Police, who arrived within five minutes of being called, used a Taser electric shock gun while detaining the 19-year-old suspect. He was later arrested on suspicion of murder.
The investigation is being handled by the homicide command with support from the counter-terrorism officers, Rowley said.
The woman was treated at the scene but was pronounced dead a short time later. The other injured people - one woman and four men - were treated in hospital and three were later discharged.
A Reuters reporter at the scene said the southern part of the square, which sits at the heart of London's university area and is close to landmarks such as the British Museum, was cordoned off by police.
A forensic tent had been erected on the pavement, the scene of the attack.
Britain says its terrorist attack threat level remains at "severe", the second-highest level, meaning a strike is "highly likely". Police had already promised to deploy more armed officers in the capital after a spate of deadly attacks in France, Germany and Belgium.
Attacks across Europe have heightened tensions between some communities, raised questions about the European Union's border policies and bolstered support for anti-EU far-right groups.
Police chiefs and security bosses have repeatedly warned that Islamic State fighters want to carry out attacks against Britain, a close ally of the United States.
London's Sadiq Khan, the first Muslim mayor of a major Western capital, called for vigilance.
"The safety of all Londoners is my number one priority and my heart goes out to the victims of the incident in Russell Square and their loved ones," he said.
"I urge all Londoners to remain calm and vigilant. Please report anything suspicious to the police. 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."
Just hours before the Russell Square attack, London's police chief said that he would deploy an additional 600 armed officers across the capital to protect against any attacks.
Flanked by heavily armed officers in full body armor, Police Commissioner Bernard Hogan-Howe said on Wednesday that it would be foolish to ignore the recent spate of attacks in France, Germany and Belgium.
London counter-terrorism police chiefs have previously warned that Islamic State was seeking to radicalize vulnerable people with mental health issues to carry out attacks. In some operations, police commanders have taken advice from specialist psychologists.
London was hit by coordinated suicide bombings on July 7, 2005, when four Islamist extremists targeted three underground trains and one bus, killing 52 people.
One of the bombs was detonated on an underground train traveling between Kings Cross and Russell Square while another bomb was detonated on a bus in Tavistock Square, a short distance from Russell Square.
Since then, dozens of plots have been foiled and there have been smaller-scale attacks, such as the killing of an off-duty soldier on a street in south London by two extremists in May 2013.
A man who attacked passengers at a London underground train station in December was jailed for life earlier this month. The judge said the attacker was suffering from paranoid schizophrenia at the time of the offence but that he may have been motivated by events in Syria.
"Londoners will wake up and in the morning they will notice an increased police presence on the streets, including armed officers," Assistant Commissioner Rowley said.
"This is there to provide reassurance and safety. We ask the public to remain calm, vigilant and alert," he said.