The 24-year-old, currently sidelined by a knee injury, was also handed a further A$20,000 (£13,000) fine and three-match ban suspended for two years by a disciplinary tribunal in Sydney.
Cooper said in a TV interview last month he would not play for Australia unless changes were made to the "toxic environment" surrounding the team, which he felt was "destroying" him.
After first making the "toxic" allegation on Twitter, Cooper then used the TV interview to attack the defensive tactics of coach Robbie Deans and criticise the lack of a dedicated training facility for the Wallabies.
A quarter of the fine handed down on Wednesday was for criticising an ARU-licensed computer game on Twitter.
"I had a fair hearing and I am very happy with the outcome," he said at ARU headquarters.
"I understand I have fallen way below par for what it means to be a Wallaby and just want to apologise to the supporters.
"I am looking forward to the future and to hopefully a big year for not only my state but for the Wallabies."
At his best an inspired player whose unpredictability can unlock the game's increasingly tight defences, Cooper helped Queensland to the Super Rugby title and Australia to a first Tri-Nations crown in a decade last year.
The New Zealand-born playmaker's contract with the ARU expires at the end of the year and he has not signed a new deal despite agreeing to stay an extra three years in Super Rugby with the Reds.
"ARU placed contract negotiations with Quade Cooper on hold until the tribunal process had been finalised," ARU deputy chief executive Matt Carroll said in a statement.
"Given the Tribunal has handed down its decision, this matter as far as we are concerned has been finalised.
"ARU will now look at how we address the contract situation involving Quade Cooper."
Cooper has repeatedly expressed his desire to play alongside All Black Sonny Bill Williams, who is expected to return to rugby league with the Sydney Roosters next year.
Cooper was fined A$6,500 by the ARU for bringing the game into disrepute after breaking the window of a taxi in 2009.
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