Scotland Yard said that "a number of pedestrians have been injured" 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 arrested at the scene."
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 children.
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 restrained on the ground in the middle of Exhibition Road.
None of the four people around him are in uniform.
Behind them is a black Toyota car with its driver's door open, which appears to have collided with a silver Vauxhall saloon.
The Natural History Museum tweeted: "There's been a serious incident outside the Museum. We are working w/ @metpoliceuk and will provide an update when we have more information."