Stokes fell foul of Article 2.1.4 of the ICC Code of Conduct for Players and Player Support Personnel, which relates to "using language or a gesture that is obscene, offensive or insulting during an International Match".
The charge was brought by on-field umpires Kumar Dharmasena and John Ward, third umpire Ranmore Martinesz and reserve umpire Simon Fry following the incident in the 42nd over of the match, which England won by 57 runs.
Stokes, who claimed four wickets and hit 70 runs as England's barren run Down Under came to an end, admitted the offence on Friday evening before accepting the sanction proposed by Andy Pycroft of the Emirates Elite Panel of ICC Match Referees.
Mr Pycroft said: "Mr Stokes' reaction was a clear breach of the Code, as players are expected to respect their opponents at all times, no matter what the match situation is. This is a cornerstone of how we play the game."