Stone said on Twitter Friday his gritty rewrite of the script for the biopic was not well received by the producers, so he made the decision to pull out.
In his Tweet, Stone said his script raised "issues of adultery, conflicts within the (civil rights) movement."
Entertainment Weekly said it was unclear how Stone's departure would affect Jamie Foxx, who is cast in the lead role.
The King project is being produced by Warner Bros. and DreamWorks, with Steven Spielberg among the individual producers, Daily Variety said.
Stone, an 11-time Oscar nominee, won Academy Awards for writing "Midnight Express" and for directing "Platoon" and "Born on the Fourth of July."