The 27-year-old from Eastern Province, smashed the stumps after hitting the winning boundary in South Africa's nail-biting one-wicket win over Sri Lanka in the Super Eight match at the Guyana National stadium here on Wednesday.
"Peterson has been officially reprimanded for breaching the International Cricket Council Code of Conduct during the World Cup match against Sri Lanka," the ICC said in a statement.
Peterson, playing in his 34th one-day international, was wicketless in his five overs in Sri Lanka's 209 all out.
He went to the crease after Sri Lanka paceman Lasith Malinga took four wickets off as many balls to set up an intriguing finish.
Peterson survied four deliveries off Malinga and in his next over hit the winning boundary.
In celebration, the South African demolished the stumps at the striker's end.
"Peterson immediately pleaded guilty to abuse of cricket equipment fixtures and fittings in a hearing the following day after play concluded in Georgetown on Wednesday," said ICC.
"Peterson admitted to have breached 1.2 of the ICC Code which relates to actions outside the course of normal cricket such as hitting or kicking the wickets.
"Petersons attitude in response to the breach was appreciated realising his momentary mistake in the heat of the moment after a dramatic finish. He apologized to the umpires on the field after the incident," said match referee Jeff Crowe.
"It was reiterated by the umpires there was no malice in his actions but there is a responsibility to maintain standards of behaviour as well as potentially damaging the costly stump cameras," said Crowe, former New Zealand captain.
"Also, I accepted that it was a momentary mistake in the heat of the moment, an out-pouring of relief after a tense and dramatic finish to the match."
"However, all players have a responsibility to maintain the highest standard of behaviour, no matter what the situation, as that is part and parcel of being a high-profile sportsman and hitting the stumps with the bat is not acceptable at any time."