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A Six Nations statement said the 29-year-old Marler had infringed Law 9.27 which includes "grabbing, twisting or squeezing the genitals" of an opponent.
Marler's team mate Courtney Lawes has also been cited under Law 9.13 for a dangerous tackle on Wyn Jones.
Both players will appear before a disciplinary hearing in Dublin on Thursday.
The incident involving Marler has received widespread coverage with former England coach Clive Woodward claiming it has brought "embarrassment" on the team.
"You can be a great player, a character and different but don't go around being a distraction and embarrassment to the team, shirt and country," Woodward, who coached England to World Cup glory in 2003, wrote in his Daily Mail column.
"I knew England were in big trouble before the World Cup final (last year) when Joe Marler started horsing around at a bizarre press conference with Dan Cole. That was embarrassing, disrespectful and said much about the team's mindset.
"I wouldn't stand for that and... nor should the team. We saw it again with his ridiculous groping at Jones' genitalia... perhaps he thinks it's clever... but it'll be interesting to see how the Rugby Football Union handle this. I know what I'd do."
England won 33-30 despite having Manu Tuilagi red-carded late on for a dangerous tackle on George North -- a decision described as "rubbish" by coach Eddie Jones.
Tuilagi faces a disciplinary hearing under Law 9.16 that states 'a player must not charge or knock down an opponent carrying the ball without attempting to grasp that player'.
England's win took them to 13 points from four games, level at the top of the table with France who were beaten by Scotland on Sunday.
Their final game against Italy in Rome has been postponed due to the coronavirus outbreak.