Video footage shared on social media showed a large police presence near Oxford Circus following the incident. One person claimed to have seen a "horrific stabbing".
A statement from the Met Police said: "Police were called shortly before 20:00hrs on Thursday, 1 July to reports of a man stabbed on Oxford Circus, close to Regent Street, W1.
"Officers, the London Ambulance Service and London’s Air Ambulance attended.
"The victim [no further details] was taken to a central London hospital where he remains in a critical condition.
"A 25-year-old man was arrested after he was detained by members of the public at the scene.
"He has been taken to a south London hospital for treatment to a head injury, which is not believed to be life-threatening.
"A crime scene is in place and officers remain in the area."
Police said the incident was not being treated as terrorism-related at this time.
Anyone who witnessed the incident or who captured video footage have been asked to contact police via 101 quoting reference Cad 7129/01Jul.
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Meanwhile, Jambusters warned of traffic in the area and tweeted: "A4201 Oxford Circus (All Directions) - Closed because of a police incident.
"Use an alternative route.
"Traffic is moderate on diversion. Expect some delay."
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Footage shared on social media showed London buses lined up in all directions during the incident.
Tube passengers were also told to evacuate with the underground station closed at the time.
One person tweeted: "What on earth is happening at Oxford Circus?!
"Just got rushed out of tube station due to a reported emergency and police and sirens everywhere!"
Transport for London confirmed the station was closed while they responded to a security alert.
However, firefighters said they were investigating a "fire alarm".
This incident comes just hours after a 16-year-old boy was stabbed to death in Croydon.
Police say they were called to a disturbance inside a home on the Shrublands estate and the boy was found injured inside.
A spokesman for the force said: "Police were called at 12.46am on Thursday, July 1 to reports of a disturbance at a residential address on Bracken Avenue in Shrublands, Croydon.
"Officers attended and found a 16-year-old male [no further details] inside suffering from stab injuries.
"They provided first aid prior to the arrival of the London Ambulance Service and London’s Air Ambulance.
"Despite their efforts, the man was pronounced dead at the scene at 1.34am. Next of kin have been informed.
"Formal identification has not taken place. A post-mortem examination will be held in due course."