Clarke was found to have breached Article 2.1.4 of the ICC Code of Conduct which relates to "using language or a gesture that is obscene, offensive or insulting during an International Match".
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. All Level 1 breaches for this offence carry a penalty of a warning/reprimand and/or the imposition of a fine up to 50 per cent of the applicable match fee, an ICC statement said.