Cabinet Secretary Sir Jeremy Heywood confirmed the decision in a letter to shadow home secretary Yvette Cooper.
He explained that no inquiry was needed as Mr Mitchell had apologised for his comments and the officer involved did not wish to pursue the matter.
David Cameron had backed his minister after he made a public apology.
In the letter, Sir Jeremy stated that he discussed the matter with Metropolitan Police Commissioner Bernard Hogan-Howe.
He wrote: “Like the prime minister he is obviously very disappointed at the lack of respect shown towards the police and agrees that the behaviour fell short of what the police should expect, in particular from members of the government.
“However, in the light of the apology given, and also the fact that the officer concerned has accepted the apology and does not wish to pursue the matter further, the Metropolitan Police Commissioner reiterated that no further action would be taken.”
The country’s top civil servant added that “Neither the prime minister nor I see any purpose in a further investigation”.
Earlier, Mr Mitchell told reporters he was sorry for not showing enough respect to the police, but maintained that he “did not use the words attributed to me”.
He said he wanted to “draw a line” under last Wednesday’s incident.
The Police Federation and Labour had both called for an inquiry, while some Lib Dems were unimpressed by the statement.
Mr Mitchell is reported to have sworn at an officer during the incident on Wednesday evening – when police directed him away from the main gate to a smaller pedestrian gate – and said “learn your place” and “you don’t run this government”.
In his first statement to reporters about the incident, on Monday morning, Mr Mitchell said that the incident had come at the end of a “long and extremely frustrating day”.
He added: “I didn’t show them the amount of respect I should have done.”
He said the police officer involved had accepted his apology.
When asked whether he had used the word “plebs”, as is alleged in the Sun newspaper, Mr Mitchell did not answer directly, saying only that he had not used the words that have been reported.
The newspaper says it has seen the official police report of the incident, which does include the word.
The issue dominated the prime minister’s official spokesman’s lobby briefing on Monday, especially the apparently conflicting accounts given by Mr Mitchell and by the police.
Asked about the differences, the spokesman said the PM “obviously accepts the statement” from Mr Mitchell.
It has also emerged that the Metropolitan Police is investigating how police records of the incident were obtained by the newspaper.
Deputy Prime Minister Nick Clegg – who had called for Mr Mitchell to give a full account of the row – said Mr Mitchell had been right to apologise and show contrition.
He said: “Being discourteous is a bad thing. He said the police officer has accepted his apology, which is significant. It is discourteous and just wrong to be rude to police officers.”
Former Lib Dem leader Sir Menzies Campbell said: “If Andrew Mitchell’s determination was to draw two lines under this matter he hasn’t achieved it.”
And fellow Lib Dem Jeremy Browne, a Home Office minister, said: “I think people want to know what was said… explaining to the media what was not said, is not the same as explaining to the media what was said.”
Business Secretary Vince Cable worked in a joke about the row during his speech to the Lib Dem conference, referring to David Cameron and Boris Johnson’s school days at Eton, before adding: “I’ve been told that jokes about social class are not good for the unity of the coalition. But as a mere pleb, I couldn’t resist it.”
I am astonished by the comments of Andrew Mitchell but not surprised by the comments of a leading Tory MP from the Nasty Party he should resign forthwith he should be setting an example to the public. Lets turn the table around for one minute if a policeman had said that to a MP the said MP would be calling for him to be disciplined by his bosses and possible sack from his job.
Coun Jones called on Mr Bennett to explain “whose side you are on” and whether he supported widespread police dismay at the incident, or whether he backed Mr Mitchell.
In a second letter to Mr Bennett this week, Coun Jones said he was giving the Tory candidate a chance to correct his “weak” response to his first letter, which resulted in Mr Bennett defending Mr Mitchell as “only human” and dismissing the Downing Street tirade as a “moment of anger”.
Coun Jones said in the letter: “I found your response disturbing since you seem to excuse Mr. Mitchell. This is not an acceptable answer from someone who hopes to lead the police in the West Midlands.
“However, I understand that in your haste to reply to me you may have confused your loyalties between the Police and Andrew Mitchell.
“I am therefore writing to give you a second chance to make clear whose side you are on?
“So, can you please give me your considered response to the question whether you back Andrew Mitchell or the police?”
Labour upped the stakes by finding a former police officer to condemn Mr Mitchell.
Retired Wolverhampton bobbie Andy Hayburn said: “Andrew Mitchell may have said something in a moment of anger. I arrested loads of people when that happened.
“Mr Mitchell is arrogant and out of touch by persisting with the implication that the Downing Street police officers are liars. As a former police officer I was accountable to the public for my actions, he should be brought to account for his.”