- Police say one man has been detained
- A car hit people on Exhibition Road in South Kensington
- Nine people were taken to hospital and two more were treated by paramedics
- Incident 'not terror-related' police say
The Metropolitan Police have released a statement confirming that a "road traffic investigation" is under way.
The force said the injuries sustained to the 11 people were "not believed to be life-threatening or life-changing".
The detained man is under arrest, the police said, and is in custody at a north London police station.
Police have confirmed that the incident in Exhibition Road was not terror-related.
A statement from the London Ambulance Service says 11 people have been treated "mostly for leg and head injuries".
Nine were taken to hospital.
Labour leader Jeremy Corbyn says his thoughts are with those injured amid "very concerning reports".
Home Affairs Correspondent
We've been to the south end of Exhibition Road nearest the Tube and the area, normally a busy destination for Saturday afternoon dining by locals and tourists, is deserted.
Eyewitnesses told us that police came rushing into each bar and restaurant and told people to get out.
We can see coats on chairs - some knocked over - half-eaten meals and half drunk glasses of wine.
Police helped one restaurant owner to recover staff belongings, like house keys, because its unclear when the area will reopen.
Eyewitness Ellie Mackay, who lives opposite South Kensington Tube station, said she heard "a couple of loud bangs" after a car hit people near the Natural History Museum.
She described the speed of the emergency services' response as "amazing".
Forensic officers are at the scene - which has been cordoned off - gathering photographic evidence.
BBC journalist Tim Stokes is at the scene:
"On a normal Saturday this area is packed with tourists but this afternoon the road is empty except for dozens of police vehicles and officers.
"Behind them, two officers stand holding guns while a police helicopter circles overhead.
"Onlookers wait with TV reporters, uncertain about what has happened.
"An Irish couple who have travelled to London for the day speak to their family on their phones, reassuring them everything is fine."
Connor Honeyman, who was in the queue for the museum, said he heard a "horrible thudding noise" before people started screaming and running inside.
He said: "We ran in, everyone was following us, and then all the security guards ran out and they closed the main entrance.
"There was much confusion before the police got there."
Damien Hackett was on his way to the Natural History Museum and witnessed the aftermath of the incident.
He said: "Everyone was instructed to get out of there now"
This was the scene a short time ago outside the V&A Museum, which is close to the scene of the crash.
The Met Police has not indicated any more details about the nature of the incident, saying they will make another statement only when they have "accurate" information.
The neighbouring Science Museum is open but, on advice from the Metropolitan Police, additional visitors are not being admitted.
An eyewitness said: "We were walking near the Science Museum and heard a bang, bang... at first I thought it was gunfire.
"Then we walked past the scene of the accident and saw a guy pinned down by other men and lots of people calling the police.
"There didn't appear to be many people hurt - a few sat by the side of the road but more looking shaken than anything."
Witnesses filmed police pinning a man to the ground near the museum.
This is the car that crashed on Exhibition Road, near the Natural History Museum.
A BBC reporter at the scene said police told her the pedestrians hit by the car sustained minor injuries.
Armed police officers are at the scene in South Kensington.
A man who was at the scene in the minutes after the crash described seeing tables being knocked over and people screaming.
He said: "Police were adamant everyone was gone from that area immediately.
"One policeman shouted 'run and don't stop running'."
The BBC's Richard Lister, who is at the scene, says the Natural History Museum has been evacuated and closed, and that other museums in the area have also been evacuated.
South Kensington Underground station is closed, he added, but other tube stations in the area remain open.
Photographs are beginning to come through of the police presence in Exhibition Road and the surrounding area.
Downing Street says Prime Minister Theresa May is being kept up to date on events.
BBC reporter Chloe Hayward describes what she saw at the scene after the incident.
A witness, who did not want to be named, said: "We heard what I thought was gunshots and saw a car drive over the pavement.
"We just ran. My friend dived on the floor and cut her hands."
Police closed Exhibition Road after the incident, which took place at 2.20pm.
A car has been involved in a collision near the Natural History Museum leaving a "number" of pedestrians injured.
The Metropolitan Police said one person had been detained following the incident in Exhibition Road, South Kensington.
It added the man was with officers but had not been formally arrested.
Inquiries are under way to establish the circumstances of the crash.
We'll keep you informed here with the latest updates.