Shops were being evacuated around the iconic bridge, where an "enormous" police cordon was in place, while a nearby university has been closed down, 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.
It also said that several people were stabbed in the incident, which evoked memories of the 2017 terror attack on London Bridge when a van was deliberately driven into pedestr before its three occupants ran to the nearby Borough Market area and began stabbing people in and around restaurants and pubs, leaving eight people dead and 48 injured. The attackers, who claimed allegiance to the Islamic State, were shot dead by the police.
Urging people to use "common sense and restraint" while circulating pictures and videos of the incident, the police said the public and the media "can help us by sending any images or footage they may have taken at the scene to www.ukpoliceimageappeal.co.uk" and anyone with information that could assist the investigation should call the Anti-Terrorist Hotline.
The Met Police said its personnel 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 in 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 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 away from him, having apparently retrieved a large knife.
The BBC also quoted a woman passenger on a bus crossing the bridge that she had seen police grappling with a "tall bearded man", and wrestling him to the ground, before he pulled back his coat to show that he was wearing "some kind of vest", which made police retreat from him.
Addressing the press later, Assistant Commissioner Neil Basu, however, said the police could confirm that "a device that was strapped to the body of the suspect is a hoax explosive device".
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.
Labour leader Jeremy Corbyn tweeted: "Shocking reports from London Bridge. My thoughts are with those caught up in the incident. Thank you to the police and emergency services who are responding."
London Mayor Sadiq Khan, who said that he was "in close contact with the Met Commissioner" over the incident, said in a statement that his "heart goes out" to those injured in "today's horrific attack".
"We must and we will stay resolute in our determination to stand strong and united in the face of terror. Those who seek to attack us and divide us will never succeed," he asserted.
The police have 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 )