FIFA's plan was to raise up to $4.2 billion by selling about a 20% stake in a new unit that would run FIFA events, including the World Cup, valuing it at $20 billion.
The proposal, first announced on Tuesday, was strongly opposed by European soccer's governing body, UEFA, which threatened a boycott and accused FIFA of putting the sport's "soul" up for sale.
"Having listened carefully to all the views, it has become clear that the project has created divisions of a nature that, regardless of the level of support, are no longer in the interest of the objective set out in the first place," FIFA President Gianni Infantino said in a statement.
"Our purpose has always been - and will always be - to unite and improve. As a result, this proposal will not proceed.
"Moving forward, my intent is to bring all interested parties back together in the coming days and weeks in the spirit of shared interest in our game, and with the objective to continue growing football everywhere, particularly in those countries that mostly need our support.
Earlier on Friday, Infantino's senior adviser Carlos Cordeiro resigned with immediate effect, calling the plan "a bad deal for football".
FIFA's Chief Operating Officer Kevin Lamour said staff were "deceived" by Infantino, describing the proposal as a "project of one person".
British Prime Minister Andy Burnham, meanwhile, told reporters on Friday that Infantino was "the wrong man to lead the organisation".
