He has been taken to a south London police station where he remains in police custody.
The auto left the road and hit into the group before coming to a stop at barriers outside the building at about 7.37am local time.
Speaking shortly after the incident, Britain's counter-terrorism police chief said it appeared the incident was "a deliberate act" at an iconic site and was therefore being treated as a terrorist incident.
Several high-value locations exist in Westminster, with many important political premises in the area. It was then driven around the Westminster and Whitehall area from approximately 6am and stayed in this area until the time of the incident.
The BBC's Callum May, at the scene, said: "Parliament Square is now ringed by blue police tape".More news: Pregnant Reality Star Lyric McHenry Found Dead At 26
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The man was driving a silver hatchback.
"He made no attempt to slow down as he hit the cyclists", said Robert Nicholson, 36, who was on his way to work.
The Metropolitan Police said on Twitter: "At 7.37am today, a auto was in collision with barriers outside the Houses of Parliament. We sent a number of resources to the scene including three ambulance crews, responders in cars and an incident response officer".
"At 0737hrs today, a auto was in collision with barriers outside the Houses of Parliament".
The man collided with a number of cyclists and pedestrians before impacting the barrier. Officers remain at the scene. "On the details we have at the moment, we don't believe this individual was known to MI5 or counter-terror police".
Streets in the area were cordoned off as police rushed to the scene, eyewitness video showed.
Westminster was the scene of a terror attack last year, when Khalid Masood, a 52-year-old British convert to Islam, drove a vehicle at pedestrians on a bridge over the River Thames, before fatally stabbing a policeman on guard outside parliament.