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".
Witness Katie Craine said she was coming out of the museum when she saw a man in handcuffs pinned down by police near a damaged auto. A man was detained an now under arrest.
The statement further said that officers were on the scene, and the London Ambulance Service has been called.
"Inquiries to establish the circumstances and motive are underway", London Police said. Their injuries are not thought to be life threatening.
It is also believed that a number of pedestrians have been injured in the incident. Witnesses said it would never have had a chance of hitting large crowds with the bollards so obviously in its path, so it would not have been a likely terror attack.
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The woman, who did not want to give his name, said: "When everything died down a bit, we went back to the place where he was, and saw that on the ground lay a man, whom the police hold".
The incident happened around 2.20pm London time (10:20pm WA time) in Exhibition Rd, South Kensington.
The Natural History Museum is the fourth most popular tourist attraction in the United Kingdom, boasting as estimated 4.6 million visist during 2016, according to the Association of /leading Visitor Attractions.
Security is high in Britain after five terror attacks since March - four of them in London and one in Manchester - with the bloodshed claiming 35 lives.
London Ambulance Service said the people it treated - including the suspected driver - had mostly sustained head and leg injuries. Masood acted alone, police said, but may have been inspired by ISIS.
Crowds in the busy tourist spot in South Kensington, which is also home to the Victoria & Albert Museum and the Science Museum, fled screaming in panic, an AFP reporter said.