Police said they were treating the stabbing at Leytonstone station as a terrorist incident.
One man sustained serious injuries not considered to be life-threatening, police said. Two others suffered minor injuries.
The suspect was taken to a London police station.
Police said they were called just after 7 p.m. to reports of a number of people stabbed at the station and a man threatening others with a knife.
Commander Richard Walton, who leads the Met's Counter Terrorism Command, said: "We are treating this as a terrorist incident."
"I would urge the public to remain calm, but alert and vigilant. The threat from terrorism remains at severe, which means that a terrorist attack is highly likely."
UK faces terrorist threat
Police released no information about the man's identity or possible motive, but the United Kingdom is facing stepped-up threats from ISIS -- especially after British fighter planes began flying sorties against ISIS targets in Syria this week.
Intelligence obtained by European security agencies indicates ISIS is aiming to attack the United Kingdom
as a follow-up to its attacks in Paris last month, a senior European counterterrorism official told CNN.
The Tube, also called the London Underground, is the city's subway system. It has 270 stations on 11 lines that stretch a total of 250 miles.
In 2005, suicide bombers attacked three Underground trains and a double-decker bus
in a coordinated attack that left 52 people dead and more than 770 wounded. A British al Qaeda operative planned the bombings, according to internal al Qaeda documents that surfaced in 2012
Videos show arrest
Videos posted to YouTube and on Twitter purport to show the aftermath of Saturday's London stabbing. A large pool of blood is on the ground near the exit gates.
Several show police confronting a man in the ticket area, near the exit, and yelling, "Drop it! Right now!"
They fire a stun gun at the man, who is wearing a gray top, tan pants and a black hat with ear flaps. But the man continues pacing in front of the officers and even lunges at them.
In one video, a woman can be heard saying, "I just want to get out of here." The scene is loud, with voices echoing throughout the station and police repeatedly shouting at people to get back.
There is more shouting before a pop is heard, apparently from the stun gun, and the man falls to the ground. Someone watching shouts, "Yes! Stupid idiot!"
Two police officers roll the man onto his stomach and handcuff him.
A man in the crowd shouts, "You ain't no Muslim, bruv! You're no Muslim, bruv! You ain't no Muslim!"
Hours later, the station was still roped off with blue and white police tape and police officers were standing guard outside. Investigators wearing protective clothing occasionally went in and out.
Leytonstone is on the Central line, which runs roughly west to east through central London and into the northeastern suburbs.
Transport for London, which runs the Underground, shut down a large part of the eastern Central line after the incident.