The Liverpool boss sprinted onto the pitch to hug with Alisson after Divock Origi headed home a dramatic 96th minute winner against Everton.
It is understood the German is set to be fined by the FA and is not facing a touchline ban.
An FA statement said: "Jurgen Klopp has been charged with misconduct relating to his behaviour in the 96th minute of the game between Liverpool and Everton yesterday [2 December 2018].
Klopp apologised following the final whistle as he failed to control his emotions as the Reds closed the gap on Manchester City to two points.
The 51-year-old said: "I have to apologise for my run. I apologised immediately after to Marco (Silva), I didn’t want to be disrespectful.
“I couldn’t stop myself. If I could describe it I could probably control it.
“My respect to Everton could not be bigger after that game. We’ve scored late on before but today, with the intensity.
“The plan was not to run, then I stopped and I was close to Alisson. he was surprised, you should have seen his eyes!”
Club legend John Arne Riise tweeted his delight at the German's reaction, as he said: "And I love Mr Klopp even more after that celebration."
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