The nearby Westminster subway station was closed, with police asking people to stay away from the area.
There was nobody else in the vehicle and no weapons have been recovered at this stage.
Video posted to Twitter by Euronews/NBC UK journalist Vincent McAviney shows heavily armed police at the scene as the man is led from the auto in handcuffs.
Neil Basu, Assistant Commissioner Specialist Operations at the Metropolitan Police, said that the incident "appears to be a deliberate attack" and officers from the Counter Terrorism Command are leading the investigation.
Nigel Evans, a Conservative member of Parliament, told TalkRadio that "filtering traffic" in the area could add an extra layer of security.
Security around Parliament has been increased since an attack at the complex in March 2017 when four people died.
The suspect arrested after following yesterday's Westminster terror attack has been named as Salih Khater.
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The session of the COBRA committee was called after a motorist slammed into pedestrians and cyclists before hitting a barrier near the House of Lords on Tuesday.
The man, identified as 29-year-old Sudanese immigrant Salih Khater, was arrested after crashing a silver Ford Fiesta into cyclists and pedestrians outside the Houses of Parliament on Tuesday morning.
The Houses of Parliament have large steel and concrete security barriers, which stopped the auto.
Masood abandoned his vehicle then stabbed and killed unarmed Pc Keith Palmer before he was shot by armed police in a courtyard outside Parliament.
But among those to express their shock at the keen footballer's arrest was Anwar Mukhta, who said he has known the suspect for eight years. Reports indicate at least some of the injured were cyclists. He was shot dead. I heard some noise and someone screamed.
"I saw smoke coming out of the vehicle".
Prime Minister Theresa May, now on holiday in Switzerland, tweeted that her "thoughts are with those injured in the incident in Westminster".
Armed police have swooped on the area, cordoning off streets around Parliament Square, Millbank and Victoria Tower Gardens.