The incident caused panic on the crowded street outside the museum on Saturday afternoon.
Britain has been on a "severe" terrorist threat level and a massive police response followed the traffic incident.
Workers in a cafe near London's Natural History Museum said they fled the scene in panic after the crash.
Marilin Mueller, 20, said she thought at first it was a traffic accident but that "loads of police cars" arrived shortly after. She says "all of these police came marching down saying, 'Move, move.' They said, 'you need to evacuate.'"
Dieon Rurora said people were running down the street to get away and some fell over. He says "It was quite scary."
Many shops in the museum district were evacuated and the museum was shut down as police tried to determine if there was a threat to the public.
London Mayor Sadiq Khan has tweeted that "a number of people" have been injured in an incident involving a car in the city's museum area.
He said "details are still emerging" about the incident yesterday and that he is in close contact with Assistant Metropolitan Police Commissioner Mark Rowley, who plays a lead role in the police's counter-terrorism operation.
- AP
