Eleven individuals were treated at the scene, primarily for leg and head injuries, with 9 carried to a hospital, according to the London Ambulance Service.
No one is believed to have life-threatening or life-changing injuries, and the majority were discharged by late Saturday.
However, Metropolitan Police said in a statement that although their inquiries continue, the incident outside the museum was being treated as a road traffic collision and was not terror-related. The crash occurred around 2:20 p.m. outside the London Museum of Natural History, a popular tourist destination. Helicopters buzzed overhead as ambulances rushed to the scene.
British Prime Minister Theresa May thanked the first responders and the public for their help and said her thoughts were with the injured.
Nearby museums have been evacuated and the London Underground has been closed between Embankment and South Kensington. Video of the immediate aftermath posted to Twitter showed men holding the driver against the ground as pedestrians continued to mill around.
The museum confirmed the incident on Twitter and said it is working with the police.
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The auto ran into other vehicles and a large concrete barrier of the sort installed widely across central London after terrorist attacks on Westminster Bridge, Borough Market and The Mall where vehicles have driven into crowds. The attack killed eight people and injured more than 40 others, CNN reported. The attackers were fatally shot by police.
Three of the attacks in London involved the use of a vehicle to run down pedestrians. A man was detained an now under arrest.
In March, a man drove into pedestrians on Westminster Bridge, killing four people.
A BBC reporter at the scene said that she saw a vehicle moving "diagonally" across the road before the crash.
The paramedics are on the spot and have been giving medical treatment to the injured people.
Det Con Darren Case, from the force's roads and transport team, said he appreciated "the concern and alarm this incident caused".