A constable in the Diplomatic Protection Group was held on Saturday evening and bailed yesterday to return next month, Scotland Yard said.
Mr Mitchell resigned in October after weeks of controversy over what he was reported to have said to police after being told he could not ride his bike through the main gates.
On resigning, he insisted in a letter to Prime Minister David Cameron that he had not referred to an officer on the gate as either a "pleb" or a "moron" but acknowledged delivering the parting line: "I thought you guys were supposed to f****** help us."
The story first emerged in The Sun and transcripts of what was allegedly said appeared later in the Daily Telegraph.
Scotland Yard said that on Thursday the Metropolitan Police Service (MPS) received fresh information regarding the alleged unauthorised disclosure of information.
As the result of this the Directorate of Professional Standards arrested a police constable in the Diplomatic Protection Group, on suspicion of misconduct in a public office, at 8.15pm on Saturday. He was bailed yesterday morning to return in January. He has been suspended from duty.
The matter will be formally referred to the Independent Police Complaints Commission today.
The Yard's statement said the arrest was linked to previous inquiries by the MPS as to how internal information was obtained by national newspapers following an incident at Downing Street in September.
"These inquiries found no evidence to suggest any of the officers involved in the incident were involved in the unauthorised release of information.
"The officer arrested was not on duty at the time of the incident in Downing Street."
When he resigned Mr Mitchell admitted the row over the incident made his position untenable.
He said it was not fair to put his colleagues and family through such "damaging" stories any longer.
He had clung desperately to his position amid a mounting clamour lasting a month for him to go.
He did not attend the Conservative Party conference in Birmingham - neighbouring his Sutton Coldfield constituency - after admitting his presence would be a distraction.
He sought - and failed - to win over Police Federation members by meeting them in his constituency and trying to explain his actions.
He told Mr Cameron: "I have made clear to you - and I give you my categorical assurance again - that I did not, never have, and never would call a police officer a 'pleb' or a 'moron' or used any of the other pejorative descriptions attributed to me."
But he accepted it was "obviously wrong of me to use such bad language and I am very sorry about it and grateful to the police officer for accepting my apology".
Mr Cameron said he was sorry to receive Mr Mitchell's letter but added: "I understand why you have reached the conclusion that you have, and why you have decided to resign from the Government.
"I regret that this has become necessary, and am very grateful for all you have done, both in Government and in opposition."