Police said 11 people were injured when a vehicle apparently mounted the pavement and hit pedestrians.
Mirror reports that the vehicle mounted the pavement before hitting the pedestrians. "At this point in investigation, we don't see accident as a terrorist incident", a spokesman for Scotland Yard told Guardian.
The Natural History Museum, a few blocks away from Hyde Park, is popular with locals and tourists alike and the area was busy with pedestrians braving a chilly autumn day in London.
Police have put the area on lockdown, with a large security presence in the area quickly after the incident.
British Prime Minister Theresa May was being updated on the incident, according to her office.
"Inquiries to establish the circumstances and motive are underway", London Police said.
Police said a number of people were injured and one person was detained at the scene.
Authorities did not immediately disclose the number of injured people or the severity of their injuries.
In a statement, London Mayor Sadiq Khan said he was in contact with Assistant Metropolitan Police Commissioner Mark Rowley.
The incident comes as the terror threat level in Britain is at "severe", its second-highest level, meaning that an attack is likely.
Officers had arrested a man at the scene and he was now being questioned.
The Natural History Museum is located on Cromwell Road and Exhibition Road in South Kensington in south west London. "My thoughts are with the injured".
The UK has suffered a number of terror attacks this year, including two auto attacks in London at Westminster Bridge and London Bridge and a bombing outside the Manchester Arena, in which 22 people were killed.
In March, a man drove into pedestrians on Westminster Bridge, killing four people.
Nine people were taken to area hospitals, officials told the BBC.
A police forensics officer in blue coveralls is outside the Natural History Museum in London, taking photographs of the scene where a auto hit pedestrians, injuring some people.