The 32-year-old was widely reported to have told Anderson to "get ready for a f****** broken arm" in comments picked up by the stump microphone as England's number 11 was batting on day four of Australia's victory in Brisbane.
And the International Cricket Council on Monday found Clarke breached its code of conduct by "using language or a gesture that is obscene, offensive or insulting".
A statement read: "The incident happened when Clarke made inappropriate gestures and directed an obscenity towards England's James Anderson, which was picked up by the stump microphone.
"The charge was brought by umpire Kumar Dharmasena and third umpire Marais Erasmus.
"On Monday morning, Clarke admitted the offence and accepted the sanction proposed by Jeff Crowe of the Emirates Elite Panel of ICC match referees. As such, there was no need for a formal hearing."
Clarke defended his sledging after the game, dismissing it as "banter".
He said: "Through my career, there has always been banter on the cricket field - and I cop as much as I give, that's for sure.
"That's part and parcel of the game...but all the England players know we certainly respect them, and we understand we have to be at our best to beat them.
"I've heard a lot worse said on a cricket field than what the Australia players or the England players said throughout this Test match."
The fine comes after a Test that was played amid no little rancour both on and off the field.
The tourists have been on the receiving end of a hostile reception, most notably from the press who have been particularly harsh in their treatment of England bowler Stuart Broad.
England skipper Alastair Cook, meanwhile, accused David Warner of being "disrespectful" in his description of Jonathan Trott's batsmanship as "poor" and "weak".
- Sports & Recreation
- International Cricket Council