The alleged incident occurred around the 67th minute, the FA said. Mejbri came on as a substitute in the 83rd.
"It's alleged that the player acted in breach of the Laws of the Game and/or in an improper manner and/or used abusive and/or indecent behaviour by spitting at or in the direction of Leeds United supporters ...," the FA said in a statement.
The 22-yer-old Tunisia international, who moved to Turf Moor from Manchester United last year, has until November 28 to respond.
Promoted Burnley, just above the relegation zone at 17th in the standings with 10 points from 11 matches, next host third-placed Chelsea on November 22 after the international break.