The Met Police said while the situation was yet "unclear", it was treating the incident as "terror-related".
Shops were being evacuated around the iconic bridge, where an "enormous" police cordon was in place, the BBC reported.
"At this stage, the circumstances relating to the incident at #LondonBridge remain unclear. However, as a precaution, we are currently responding to this incident as though it is terror-related.
"One man has been shot by police. We will provide further information when possible," the Metropolitan Police said in a tweet.
The police also urged people to use "common sense and restraint" while circulating pictures and videos of the incident.
According to the Met Police, cops were called to a premises near the bridge on reports of a stabbing at around 2 p.m. (GST) and had detained a man.
A BBC reporter on the spot said that he had seen a group of men involved a fight on the bridge, before the police reached the spot and shots were fired.
"There appeared to be a fight going on on the other side of the bridge, with several men attacking one man.
"Police then quickly arrived, including armed police, and then a number of shots were fired at this man," he reported.
According to the BBC, a video has emerged showing police officers aiming guns at a white lorry that jack-knifed across London Bridge, surrounding the vehicle before moving to the rear to check its container.
London buses could be seen either side of the lorry while three police cars were parked next to it on the bridge.
Another video filmed from a nearby bus showed the apparent suspect appearing to be shot as he lay on the ground, while another man in a suit and jacket could be seen running from him, having apparently retrieved a large knife.
Prime Minister Boris Johnson, in a tweet, said that he was being updated on the incident and wanted to thank the police and all emergency services for their response. He was returning from his constituency to take stock of the situation.
Home Secretary Priti Patel also tweeted that she was "very concerned" about the incident.
London Mayor Sadiq Khan said that he was "in close contact with the Met Commissioner" on the incident, and urged people in the area to follow police directions.
The police asked people to follow the directions of its personnel on the spot, while British Transport Police announced that the London Bridge station was currently closed and no trains would be stopping there.
( With inputs from IANS )