But more than three hours after the incident, police said it was not being treated as terror-related.
The Natural History Museum in a tweet confirmed the "serious" incident and said they are working with the police to get the situation in control.
The London Ambulance Service said they treated 11 people, including nine who were taken to hospital.
In June seven people were killed and over 30 more injured when a van plowed into a group of pedestrians outside of a pub near the London Bridge, before three knife-wielding suspects stabbed several patrons.
Some showed the black Toyota Prius, registered with Transport for London (TfL) as a minicab, that had collided with a silver Vauxhall saloon and a Jaguar.
"When I heard the crash, I saw people running, I saw only the vehicle, it was panic".
"There were 100-odd people running away. But I think it's okay".
Both women said the front of the vehicle was "pretty smashed up" and may have hit some nearby concrete bollards.
"The police came in and told us to evacuate There was panic".
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Police said it was believed the auto had mounted the pavement outside the popular attraction in west London and collided with a number of pedestrians. Officers are on scene, and the London Ambulance Service have been called.
A man was detained an now under arrest.
"Police have asked people to avoid the area while their inquiries continue", he said.
The Natural History Museum is in the bustling section of South Kensington, popular with both Londoners and tourists.
"The Museum's visitors and staff are always our first priority".
Here's all the info on the landmark - where it is, when it was opened and what happened in the traffic incident which saw multiple people injured by a taxi?
The road was closed to motorists as police swooped in.
Downing Street said British Prime Minister Theresa May was being briefed on the incident.
Britain has been on a "severe" terrorist threat level indicating an attack is viewed as highly likely.