The penalty was handed down by Roshan Mahanama of the Emirates Elite Panel of ICC Match Referees following a hearing that took place after the match, which Australia won by 63 runs by the D/L method to take a 2-0 lead in the five-match series.
The player was charged under clause 1.3 of the ICC Code of Conduct which refers to 'showing dissent at an umpire"s decision'.
The charge was laid by on-field umpires Asad Rauf of the Emirates Elite Panel of ICC Umpires and Norman Malcolm, as well as third umpire Billy Doctrove of the Elite Panel and fourth umpire Clyde Duncan.
The incident happened in the 23rd over of the West Indies innings when Malcolm turned down a caught behind appeal against Patrick Browne off the bowling of Michael Clarke.
Ponting, who had moved from his fielding position towards the pitch as part of his appeal, appeared dismayed by the umpire's decision and in the wake of that decision appeared to make a comment to the official.
Ponting pleaded not guilty to the charge at the post-match hearing in which video evidence was used.
Explaining his decision after the hearing, Mahanama said: "A captain needs to set the example and it"s not acceptable for any player, let alone a captain, to show dissent at an umpire"s decision. In the preamble to the Laws of Cricket the captains are expected to set the tone of a cricket match and a captain must set that tone for the rest of his team."
"Although the player pleaded not guilty, after scrutinising the video footage and taking into consideration the evidence submitted by the umpires I found that his actions were in breach of ICC"s Code of Conduct and decided to fine him 30 per cent of his match fee."