Police, together with the ambulance service, were called to reports of a stabbing shortly after 9pm.
At least five squad cars and two police vans attended the scene and large sections of the square was taped off.
The victim, who has not been identified, was found suffering with stab injuries.
Police said his injuries were not life-threatening and the incident is not being treated as terrorism.
Initial inquiries suggest that the victim and the suspect may know each other.
The man’s condition is not currently known.
Footage posted on Twitter shows emergency services in Trafalgar Square after the attack.
Another onlooker posted: “Something’s going down in Trafalgar Square … 8 police and ambulance. All roped off. Hope no-one badly hurt.”
A crime scene has been set up and road closures are in place.
Police are also asking drivers to avoid the area.
Witnesses, or anyone with information that could help the investigation, are asked to call 101 with the reference CAD 7777/21 Aug.