A photo on Twitter showed three men holding down another man near a black car.
It was unclear how many people were injured.
The Natural History Museum is in the bustling section of South Kensington, popular with both Londoners and tourists. The area was cordoned off Saturday by heavily armed police, according to video posted on social media. Helicopters buzzed overhead as ambulances rushed to the scene on Exhibition Road.
British Prime Minister Theresa May is being updated on the incident, according to her office.
In a statement, London Mayor Sadiq Khan said that details of the incident were still emerging and that he was in contact with Assistant Metropolitan Police Commissioner Mark Rowley.
A witness said a nearby Tube station was closed. A video posted to Twitter showed people running in the area.
The cause of the collision is under investigation, police said. Authorities initially said the incident did not appear to be terror-related but later added that investigators were “keeping an open mind” about the motivations behind it.
The Natural History Museum said on Twitter: “There’s been a serious incident outside the Museum. We are working w/ @metpoliceuk and will provide an update when we have more information.”
The collision raised concerns after a series of terror attacks this year in London involving vehicles ramming pedestrians.
In June, three men drove a van into pedestrians on London Bridge before going on a stabbing rampage at bars at nearby Borough Market. The attack killed eight people and injured more than 40 others. The attackers were fatally shot by police.
Later that month, a van plowed into pedestrians near a mosque in north London, killing one man and injuring 11 people. The driver, Darren Osborne, 47, a resident of Cardiff in Wales, was arrested at the scene.
In March, a man drove into pedestrians on Westminster Bridge, killing four people.
The suspect, identified as a 52-year-old British man named Khalid Masood, also stabbed an unarmed police officer. Masood then was shot dead by police.
An ISIS-affiliated news agency later claimed the extremist group was behind the attack that injured 50 people. Masood acted alone, police said, but may have been inspired by ISIS.