Klopp was sent to the stands for confronting the official after Liverpool's Mohamed Salah (30) was denied a free kick late in the second half at Anfield.
"Jurgen Klopp has been charged with a breach of FA Rule E3 following the Premier League game between Liverpool FC and Manchester City FC on Sunday (16/10/22)," the FA said in a statement.
"It is alleged that the Liverpool FC manager's behaviour during the 86th minute of this game was improper, and he has until Friday (21/10/22) to provide a response."
The decision means that the German is free to take charge of his side when they host West Ham United on Wednesday.
Liverpool are eighth in the league standings with 13 points from nine games, two points ahead of 12th-placed West Ham.
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