A pool of blood near the ticket barriers at the Leytonstone Underground station, about 6 miles (10 km) east of central London, was visible in footage posted on Twitter that also showed the suspect confronting officers at just after 1900 GMT.
Police said initial reports indicated the man had also threatened other bystanders. One man had serious knife injuries that were not thought to be life-threatening and two other people had minor injuries, police said.
"We are treating this as a terrorist incident," Richard Walton, who leads the Counter Terrorism Command at London's Metropolitan Police, said in a statement.
An eyewitness quoted by British newspapers such as The Guardian said the knifeman had appeared to claim that he was retaliating for Western attacks on Islamist militants in Syria.
"We are treating this as a terrorist incident."
Police declined to comment on those reports and it was not immediately possible to independently verify them.
The Leytonstone incident will draw parallels with the May 2013 murder of British army soldier Lee Rigby, who was hacked to death just south of the Thames River by two Muslim converts.
Britain is on its second-highest alert level of "severe", meaning a militant attack is considered highly likely, mainly due to the threat posed by Islamic State militants in Syria and Iraq who are encouraging supporters to attack the West.
After Islamic State militants claimed responsibility for the attacks on Paris last month that killed 130 people, British Prime Minister David Cameron won approval from lawmakers on Wednesday to bomb the Islamist group in Syria.
British warplanes first bombed oil fields controlled by Islamic State on Thursday.
Cameron said strikes would not increase the chances of an attack on Britain as militants already viewed Britain as a top target with seven plots foiled over the past year.
An eyewitness to the knife attack was quoted as saying the attacker had screamed about Syria.
"I just saw a lot of people running but I ignored it and kept walking to get my train, but suddenly what I saw I couldn’t believe my eyes and what I saw was a guy with a knife,” the Guardian quoted an eyewitness as saying.
"As he was coming out this is what he said: 'This is what happens when you f*** with mother Syria, all of your blood will be spilled.'"
Such apparently random attacks are extremely difficult to thwart because they require relatively little planning and very basic equipment.
In 2013, Michael Adebolajo and Michael Adebowale ran over Fusilier Rigby near Woolwich Barracks before setting upon him with knives and a meat cleaver in an attempt to behead him.
They asked bystanders to film them with bloodied hands, calmly justifying their actions as a response to Britain's foreign policy. They were jailed for life last year.
British security services say about two thirds of their time is spent countering international militants, much of that connected to Syria.
Britain suffered by far its worst militant Islamist attack in July, 2005, when 52 people were killed by suicide bombs on underground trains and a bus.
A beach attack in Tunisia in June this year that killed 30 British holidaymakers was the biggest loss of British lives in such an incident since the July 2005 London bombings.
Islamic State said on Saturday that the married couple who killed 14 people in a mass shooting in California, which US authorities are investigating as an act of terrorism, were followers of the militant group.
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