Klopp ran to the centre circle at Anfield when Divock Origi scored in the final moments to clinch a dramatic Merseyside derby victory.
He apologised to Everton manager Marco Silva for his celebration after the match and said he was not sure how the FA would respond to his actions.
Several Premier League managers have come out in support of Klopp’s celebrations, with the last-gasp victory keeping them just two points behind leaders Manchester City.
Pep Guardiola said Klopp’s reaction was “understandable”, admitting he and his adversaries have “a lot of emotions in those moments”.
Klopp has until 6 pm on December 6, 2018, to respond to the charge.