Slot was sent off after the final whistle by referee Michael Oliver in the dramatic 2-2 draw with Everton, which was the final derby clash staged at Goodison Park.
The Dutchman and his assistant Hulshoff were deemed to have "acted in an improper manner and/or used insulting and/or abusive words and/or behaviour" towards the match officials.
Liverpool and Everton have also been charged with their players behaving in an "improper and/or provocative way following the final whistle".
All parties involved have until Wednesday, February 19th to provide responses to the charges, which could bring fines and suspensions.
James Tarkowski's 98th-minute equaliser sparked wild celebrations from the home Everton fans, with some spilling onto the pitch.
Slot and Liverpool were incensed that the goal was allowed to stand, claiming a foul by Beto on defender Ibrahima Konate shortly before.
At the final whistle, Abdoulaye Doucoure appeared to celebrate in front of the visiting Liverpool fans, triggering Curtis Jones to run in his direction and shove him away.
The scuffle created a fracas between both sets of players with Doucoure and Jones sent off by referee Oliver after receiving second yellow cards.
Slot and his assistant Hulshoff were also dismissed after approaching the officials on the pitch.
It means the pair are expected to remain in the dugout when Liverpool – top of the Premier League by seven points – host Wolves at Anfield on Sunday.