The exhibition, which opens next week, contains a number of explicit pictures, including images of sado-masochism. Officials at the gallery showed police the catalogue in case it offended against pornography legislation.
The Clubs and Vice Squad police advised against the display of two photographs - one of a naked five-year-old girl sitting with her legs open, and the other of two men performing a sexual act.
The Hayward Gallery will not be including the photograph of the girl, entitled Rosie, although it had been a part of the exhibition when it toured in other countries. Officials have not yet decided whether to follow police advice on Helmut and Brooks, which shows the homo-erotic practice of "fisting".
Child-abuse charities were outraged at the prospect ofRosie going on show in London because they feared it would appeal to perverts. Esther Rantzen, chairwoman of ChildLine, called it "horrific".
A South Bank Centre spokeswoman said: "We do not have room to show the whole touring exhibition, and Rosie is not representative, or one of Mapplethorpe's best works." She added: "The climate has changed since that picture was taken in 1976 ... the issues around how children are portrayed are very different now."
The retrospective has already been exhibited in many countries, she said. Other photographs feature male genitalia, homosexual sex, whips and guns.
Mapplethorpe, who died in 1989, was a sought-after portrait photographer also famed for his still-life flower pictures. He once said: "I went into photography because it seemed like a perfect vehicle for commenting on the madness of today's existence."
The retrospective is being toured by the Robert Mapplethorpe Foundation. Its publicity says: "His graphic portrayals of sado-masochism are provocative and hard-hitting, demonstrating his fascination with the body as a site of pleasure, humiliation and pain. Vilified for their disturbing, often fiercely sexual content, the pictures are, at the same time, celebrated for confronting society's values and prejudices."