London Ambulance Service says 11 people were injured Saturday afternoon after they were hit by a auto.
BBC reporter Chloe Hayward said she was leaving the museum as the incident happened.
The Natural History Museum was sealed off with crime-scene tape and police cars, as officers tried to clear hundreds of tourists and families from the scene.
Nearby museums have been evacuated and the roads around the area have been closed, according to reports.
Armed police officers were deployed, with enquiries to establish the circumstances and motive undertaken. Police said none of the injuries were life-threatening or life-changing.
In a statement, London Mayor Sadiq Khan said he was in contact with Assistant Metropolitan Police Commissioner Mark Rowley.More news: McDonald's Szechuan sauce is coming to Athens
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There have been five attacks this year, of which three involve vehicles.
Panicky scenes ensued after the pedestrians were struck and it took almost four hours for police to reassure the anxious public that it was not another terrorist attack.
London's Metropolitan Police said they were called to the scene at 2:21 pm (1321 GMT) after reports of a collision.
The area is a popular one for tourists, given the Science Museum and the Victoria and Albert Museum are also on Exhibition Road. Prime Minister Theresa May offered her thanks to the emergency services, adding, "My thoughts are with the injured". In March, an assassin on Westminster Bridge in London was purposefully snapped into pedestrians, before he stabbed a policeman on site of Parliament.
At a time of high tension in the United Kingdom capital, the incident is not being treated as terror-related, Metropolitan Police said, calling it a "road trafficinvestigation".
Deputy Director of Operations Peter McKenna said Saturday that nine of the injured were taken to the hospital for treatment, most with leg and head injuries.
Eyewitnesses said that police rushed into each bar and restaurant in the area and told people to get out.