Both players pleaded guilty to breaking the ICC's code of conduct, it said on Friday.
The pair were found to have breached the code that relates to "inappropriate and deliberate physical contact between players in the course of play during an international match", a statement said.
The incident occurred on Thursday amid the tension of Pakistan's seven-wicket win in Abu Dhabi - which was South Africa's first test defeat in almost two years - when wicketkeeper Adnan, while trying to pick up the bail, used his shoulder and body to push Peterson, who reacted by pushing back.
"Deliberate physical contact is an action that does not belong in our game and will in no way be condoned in any situation," match referee David Boon, who issued the fines, said
Peterson played a feisty innings of 47 not out in South Africa's unsuccessful effort to stave off defeat in the first of the two-match series. The second test begins in Dubai on Wednesday.