A spokesman for the Natural History Museum told AFP: "I can confirm that there has been a vehicle collision with pedestrians on our Exhibition Road entrance".
Authorities said they are still working to establish the circumstances and motive surrounding the incident.
The arrested man was one of nine people taken to hospital following the crash, and after receiving treatment was taken for questioning at a police station.
But more than three hours after the incident, police said it was not being treated as terror-related.
Police originally said a man was arrested at the scene, but later clarified that he had only been detained.
Saturday's incident - coming so soon after vehicles were used in terror attacks in Westminster, London Bridge and Finsbury Park - initially sparked panic at the museum, an area that is popular with families.
Workers in a cafe near the Natural History Museum say they fled the scene in fear.
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". Their injuries are not thought to be life threatening.
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In footage shared on social media, police officers could be seen pinning a man on the ground in the aftermath of the incident.
Anyone with information is being urged to call the Serious Collision Investigation Unit at Merton Traffic Garage on 02085435157, or Crimestoppers anonymously on 0800 555 111. Helicopters buzzed overhead as ambulances rushed to the scene on Exhibition Road.
The UK is now under a "severe" level of threat of terror attack, according to the MI5 Security Service's rating system.
As well as the Natural History Museum, the area is also home to the Science Museum and the Victoria and Albert Museum.
Armed police were deployed to the scene and the whole area was cordoned off.
In a message later on Twitter, she said: "My thanks to the first responders at this incident this afternoon and the actions of members of the public".