A video showing police vehicles crowding the auto quickly went viral on Twitter.
The force said the crash is being treated as a "terrorist incident" and the Metropolitan Police's counter-terror command is leading the investigation.
Police said they were treating the incident as a terrorism-related and the driver, aged in his late 20s, was in custody at a south London police station. The injuries don't appear to be life-threatening, they said.
Cordons are likely to be in place for some time and Londoners have been urged to avoid the area, police said. Westminster Tube station is now closed.
"Officers remain at the scene".
People have been injured after a vehicle hit cyclists and pedestrians and crashed into security barriers outside parliament.
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Streets around Millbank, Parliament Square and Victoria Tower Gardens have been cordoned off following the crash.
Armed police swooped into the area after the incident was reported at 7.37 am local time, arresting the vehicle driver and cordoning off streets surrounding the heart of Britain's government.
Images from Sky News and social media showed a man in a puffy black jacket who was surrounded by officers before being handcuffed and led away from a silver Ford Fiesta.
In June 2017, seven people were killed and dozens injured when three men - eventually shot and killed by police - rammed pedestrians with a vehicle at London Bridge and then went on a stabbing rampage at nearby Borough Market.
Security measures in the area were reinforced after the Westminster Bridge attack in March 2017. As parliament is in recess for the summer, most lawmakers weren't using the building on Tuesday.
"It looked deliberate", he said.
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Police said that the driver of vehicle, a man, was arrested at scene after the incident which took place at 7:37 a.m. Tuesday in London. "I turned around and I saw a silver auto driving very fast close to the railings, maybe even on the pavement", she said.
He said: "I heard lots of screams and turned round".
However, the force has said it can not say if the crash was linked to terrorism and that it is keeping an "open mind".
Last year Khalid Masood murdered five people, including a police officer and injured 50, when he ploughed his auto into pedestrians in a terrorist attack. Masood then stabbed an unarmed police officer.
The crash happened at the site of an attack 18 months ago which killed five people and injured fifty others.
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Some leading figures in the USA white nationalist movement have said they won't attend or have encouraged supporters to stay away. Authorities eventually forced the crowd to disperse, but a auto later barrelled into the crowd of peaceful counterprotesters.