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Amla sustained a strain to his right quad muscle on Monday afternoon, while Peterson received stitches for a split webbing to his right hand during the second ODI on Tuesday.
"Hashim has been withdrawn from the last ODI because we felt it would be a 50-50 call with his quad strain going into the match and we didn't want to risk him with the test match against Pakistan less than a week away," Moosajee said on Tuesday.
"Robin split the webbing of the last digit of his right hand while trying to field a ball off his own bowling in the eighth over of his spell this [Tuesday] afternoon.
"He needed stitches, and will not be able to take part in the final game. Aaron Phangiso will take his place in the team."
Paceman Dale Steyn would join the squad in Potchefstroom. The selectors were expected to name a player to serve as batting cover later on Wednesday.
The Proteas lost their second consecutive ODI to New Zealand on Tuesday, suffering a 27-run loss at the Diamond Oval in Kimberley.
The Black Caps now hold an unassailable 2-0 series lead ahead of the final match of the series.
