Victory took unbeaten Liverpool to 36 points and two points behind leaders Manchester City.
"Klopp has been charged with misconduct relating to his behaviour in the 96th minute of the game between Liverpool and Everton yesterday," the FA said in a statement.
He has until 1800GMT on Thursday to respond to the charge.
Meanwhile, Liverpool striker Daniel Sturridge has been granted additional time to respond to charges of misconduct in relation to alleged breaches of its betting rules.
The charge relates to the period of January 2018 and Sturridge had been previously asked to respond on Nov. 20. The FA said on Monday it had extended the 29-year-old England international's deadline to 1800GMT on Feb. 11 next year.
FA rules prohibit players and coaches from betting on any football activity or providing non-public information to any other person that is then used for betting.
Former Manchester City midfielder Joey Barton, who served a 13-month ban for betting offences when he was a Burnley player, had urged the FA to alter their "zero-tolerance" approach to gambling in soccer after Sturridge was charged.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Christian Radnedge)
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