The lock, 29, allegedly criticised Barnes' decisions following a chaotic end to the game in Paris.
Wales conceded a try and conversion in the 100th minute as France won 20-18 to secure a third-place in the tournament.
"A hearing will be convened by Six Nations Disciplinary Panel chair, Prof. Lorne Crerar," a statement said.
Six Nations Rugby confirmed they are continuing the investigation into replacements made by France in the latter stages of the same match.
Wales coach Rob Howley was left to "question the integrity of our game" after France replaced Uini Atonio with Rabah Slimani during the 20 minutes of added time that were played.
France's team doctor said Atonio needed to go off for a head injury assessment.
France lock Yoann Maestri has received a misconduct charge for comments made about referee Wayne Barnes after their dramatic Six Nations win against Wales.