Police said it was believed a car mounted the pavement and collided with a number of pedestrians.
“The incident is a road traffic investigation and not a terrorist-related incident,” the statement said.
The museum, one of the most popular visitor attractions in the country, said in a statement: “A vehicle has collided with pedestrians near the Natural History Museum entrance at Exhibition Road.”
London’s ambulance service said they had treated 11 people, mostly for head and leg injuries, with nine taken to hospital.
Unverified footage from the scene in South Kensington, west London, showed a man being pinned to the ground by what appeared to be four security guards or police officers.
Prime Minister Theresa May was being updated, a spokesman said, adding it was usual practice in such circumstances, and London Mayor Sadiq Khan said he was in close contact with the police’s most senior counter-terrorism officer.
Packed with tourists
Exhibition Road, in one of London’s most upmarket districts, is home to a host of museums, restaurants as well as university buildings with the streets packed with tourists at the weekend.
“We heard a horrible thudding noise and a car engine. Everyone started running and screaming inside,” Connor Honeyman, who was in the queue for the museum, told the BBC.
A Reuters witness said large numbers of paramedics and police, including armed officers, were at the scene although the atmosphere appeared calm.
The car believed to have been involved in the incident was lying diagonally across the road, jammed between two other vehicles. A BBC reporter said she had seen one or two people on the ground and police had told her the injuries sustained were minor.
Britain is on its second highest security alert level, meaning an attack by militants is considered highly likely. There have been five attacks described by the authorities as terrorism this year, three involving vehicles.
In March, a man drove a car into pedestrians on London’s Westminster Bridge killing four before stabbing a police officer to death in the grounds of parliament.
Three Islamist militants drove into people on London Bridge in June before stabbing people at nearby restaurants and bars, killing eight. The same month, a van was driven into worshippers near a mosque in north London which left one man dead.
The Natural History Museum is the fourth most popular tourist attraction in the United Kingdom, with 4.6 million visits during 2016, according to the Association of Leading Visitor Attractions.
A spokesman for the museum told Reuters that no one was being allowed into the building and people were being let out through a different exit.