The man was held after an incident near the Natural History Museum (NHM) in South Kensington on Saturday afternoon.
Video footage posted on Twitter showed a man being restrained on the ground in the middle of Exhibition Road in front of what is believed to be a Toyota Prius minicab that had collided with a silver Vauxhall saloon.
Pictures and footage from the scene showed street damage and a massive police presence in the capital’s museum district, home to the NHM, the Science Museum and the Victoria and Albert Museum.
The area is a magnet for tourists, including lots of families with young children.
Downing Street said that Prime Minister Theresa May is being kept up to date with developments.
Scotland Yard said that “a number of pedestrians” were hurt in an incident in Exhibition Road in South Kensington shortly after 2.20pm.
A Metropolitan Police spokesman said: “Officers are on scene, and the London Ambulance Service have been called.
“A man has been detained at the scene.
“Inquiries to establish the circumstances and motive are under way.”
Afra Wang posted a picture of emergency services on Twitter, writing: “A crime scene? Full armed police locked the whole area out outside of @V_and_A in London. The helicopter above us doesn’t seem to leave.”
Video footage on Twitter showed a man being pinned to the ground. None of the four people around him were in uniform.
Behind them is the black Toyota with its driver’s door open.
An NHM spokeswoman said: “A vehicle has collided with pedestrians near the Natural History Museum entrance at Exhibition Road.
“The Museum’s visitors and staff are always our first priority.
“We are working with emergency services to assess the incident and we are doing all we can.”
An eyewitness at the scene said: “We were walking near the Science Museum and heard a bang, bang... at first I thought it was gunfire.
“Then we walked past the scene of the accident and saw a guy pinned down by other men and lots of people calling the police.
“There didn’t appear to be many people hurt - a few sat by the side of the road but more looking shaken than anything.
“We were then ushered into the Science Museum and the area was quickly cleared of pedestrians.”