The plans would have seen riders timed on 10 downhill sections during the three-week race, with prizes for each day and the overall fastest descender.
Belgian rider Wouter Weylandt died after crashing on a descent during stage three of the 2011 Giro d'Italia.
The 100th edition of the race begins on Friday.
"The spirit of the initiative was to highlight an important skill which is an integral part of a cycle race, without putting the riders' safety in jeopardy," said organisers RCS Sport in a statement on Wednesday.
"Rider safety is, and remains, the priority of the Giro and the race organisers."
After the initial plans were released, Dutch Team Sky rider Woet Poels tweeted that it was a "life-threatening idea", adding: "What about safety?"
Trek-Segafredo's Belgian cyclist Jasper Stuyven said organisers "should be ashamed" and that "riders will take even more risks" causing "more danger to other riders in the bunch".
RCS Sport said that reaction to the proposals suggested the classification, which was to be sponsored by tyre manufacturer Pirelli, "could be potentially misunderstood".
They added that they had therefore "decided to eliminate all such classification and prize money" but make data of descent speeds available to fans.
The Association of Professional Cyclists said it was "very happy" RCS had come to "a solution for the good of the riders".
The Giro is one of three three-week Grand Tours during the cycling season, together with the Tour de France and Vuelta a Espana.
Giro d'Italia organisers have abandoned plans for a best downhill rider category after criticism from riders that the idea was "life-threatening".