London's police force said the 23-year-old suspect was held at his home on Wednesday evening on suspicion of "intentionally encouraging or assisting the commission of an indictable offence".
The arrested man was not named and is not a police officer or a member of police staff. He was released early on Thursday after questioning.
Andrew Mitchell quit as the "Chief Whip" in charge of discipline in Cameron's parliamentary Conservative party in October following weeks of negative headlines.
He had been accused of angrily calling officers "plebs" when they refused to let him cycle through the main gates at Downing Street.
Mitchell had denied using the class-laden insult but was contradicted by a police log of the incident leaked to a newspaper.
The snobbish term was damaging for Mitchell and the Conservatives because it played into opposition claims that the government is elitist and out of touch with ordinary Britons squeezed by economic austerity.
But doubts have grown over the police account since Channel 4 News reported that a policeman posed as a member of the public and falsely claimed to have heard Mitchell use the pejorative term, in an email sent to a Conservative lawmaker.
Cameron and London's Metropolitan Police have both stressed the seriousness of the allegation, which threatens to undermine relations between police and politicians at a time when the government is cutting force budgets.
CCTV footage of the incident aired by the programme also showed that the street outside the gates was almost empty, even though the email and the police log said several people had been "shocked" by Mitchell's outburst.
A policeman working in the London force's Diplomatic Protection Group was arrested on Saturday on suspicion of misconduct. He was not on duty at the time of the Downing Street altercation.
(Reporting by Peter Griffiths and Tim Castle)