The man, in his late 20s, is being held in custody at a south London police station after armed officers swarmed the scene following the suspected terror attack just before 7.40am on Tuesday.
Two vehicles, which appear to be police vans with their lights flashing, can be seen behind the car shortly before the crash in footage of the incident aired on BBC News.
The silver Ford Fiesta is seen coming along the road next to Parliament Square before moving to turn right towards Westminster Abbey.
As an ambulance passes the car on its right-hand side, the vehicle swerves left, crossing oncoming traffic and a pavement before entering a small road and crashing into a security barrier.
A police officer can be seen jumping another barrier that runs along the side of the road to get away.
Scotland Yard, which is treating the incident as a “terrorist incident”, could not immediately comment on whether the suspect’s car was being followed at the time.
Images posted to social media showed a man, wearing a black puffer jacket, surrounded by police and being led away in handcuffs from the car
There was nobody else in the vehicle and no weapons were found, the Metropolitan Police said.
Two people were taken to hospital, while a third person with minor injuries was assessed at the scene, the London Ambulance Service (LAS) said.
Prime Minister Theresa May said her thoughts were with those injured and thanked the emergency services for their “immediate and courageous” response.
A meeting of the Government’s emergency cobra committee will be held at 2pm.
Witness Ewalina Ochab told the Press Association: “I think it looked intentional - the car drove at speed and towards the barriers.”
She continued: “I was walking on the other side (of the road). I heard some noise and someone screamed.
“I turned around and I saw a silver car driving very fast close to the railings, maybe even on the pavement.”
The car appears to have been driven through cyclists before ploughing into the security barrier.
Footage shot outside Parliament showed cyclists helping at least one rider lying on the ground as ambulance crews and armed police arrived on the scene.
Cyclist James Maker, 30, of Chelmsford, Essex, passed the scene in Westminster minutes later and saw a woman injured on the ground and the car crashed into the barrier.
“I looked to the right-hand side and there was a cyclist on the floor, clearly injured,” he told the Press Association.
“It was a woman, they were clearly quite injured, they weren’t moving and they were in the recovery position.”
Jason Williams, 45, from Kennington, was walking to work when he saw the crash.
“I saw a car going at high speed towards Parliament. It hit a bollard,” he told the Press Association.
“It looked deliberate. It didn’t look like an accident. How do you do that by accident? It was a loud bang.”
Streets around Parliament Square, Millbank and Victoria Tower Gardens were cordoned off as police, ambulances and firefighters arrived.
Bus driver Victor Ogbomo, 49, passed the scene just after the crash.
“All I saw was the smoke coming out of a vehicle, a silver vehicle ... I just stopped the bus,” he said.
“The police said we have to move back, then in less than five minutes the response team came.
“They went to the vehicle, so we had to push back. I saw the car in the barrier, I didn’t know how it got there.
“I think someone was inside the vehicle because many police went towards the vehicle.”
He said officers had their guns out when they arrested the driver.
A number of armed police officers remain stationed at a cordon beside Parliament, while Westminster Bridge and Tube station are both closed.
The cordon was widened twice and sniffer dogs were seen scanning the area.
Scotland Yard said: “”At 7.37am on Tuesday August 14, a silver Ford Fiesta collided with a number of cyclists and pedestrians, before crashing into barriers outside the Houses of Parliament.
“The driver of the car, a man in his late 20s, was arrested at the scene by armed officers.
“He has been taken to a south London police station where he remains in police custody.
“He was arrested on suspicion of terrorist offences.
“There was nobody else in the vehicle, which remains at the scene and is being searched. No weapons have been recovered at this stage.”
A force spokesman added: “At this stage, we are treating this as a terrorist incident and the Met’s Counter Terrorism Command is now leading the investigation.”
The Houses of Parliament are surrounded with security barriers of steel and concrete.
The measures were extended in the wake of the Westminster Bridge attack in March 2017 when Khalid Masood ploughed a car into crowds on Westminster Bridge, killing four people.
Masood abandoned his car then stabbed and killed unarmed Pc Keith Palmer before he was shot by armed police in a courtyard outside Parliament.
The terrorist threat against the UK is seen as unprecedented.
In addition to five attacks that occurred last year, authorities say they have stopped 13 Islamist and four extreme right-wing plots since the Westminster atrocity in March 2017.
Police and MI5 are running at least 500 live operations involving roughly 3,000 active “subjects of interest” at any one time - while there is also a wider pool of more than 20,000 individuals who have previously featured in probes whose threat must be kept under review.
Earlier this year, the Government unveiled a refreshed counter-terror strategy.
Under the blueprint, MI5 intelligence will be shared with bodies outside the security community in an attempt to stop suspects before attack plots can crystallise, while anti-terror laws are to be strengthened to allow earlier interventions.