The BBC has been told that the victim of the "phone snatching" was injured after fighting with other members of the public who stepped in to help.
An eyewitness said he saw "two or three teenagers" on a bicycle looking at a middle-aged man before they caught him wearing a knife mask.
The witness, who did not wish to be named, said passersby had joined and a man jumped off the moped and intervened during the attack.
on Thursday morning, saying that both the moped rider and the middle-aged man were stabbed. Police confirmed that the case was being treated as a suspected robbery and a search was on for two suspects.
Paramedics treated four patients at the scene, three of whom were taken to hospital, the London Ambulance Service (LAS) said. His injuries are said to be non-life-threatening.
A cordon about 50 metres (160 ft) long, at 22 Bishopgate, is placed outside the location, and is being guarded by police officers.
Inside the police tape, medical kits and clothes could first be seen spread out in small piles on the ground, and blood was visible on the pavement.
The witness said he had seen a teenager "catching up" the victim. "The next thing I saw, was this teenager catching this guy, this middle-aged man. Things grew so fast," he said.