Jadeja and Anderson were involved in an alleged altercation when the teams left the field of play for lunch at Trent Bridge on Thursday.
Anderson was handed a Level 3 charge on Tuesday evening "for allegedly abusing and pushing Ravindra Jadeja".
However, it has now been claimed by the England and Wales Cricket Board that Jadeja also played a part in the incident.
"It is alleged that after the players left the public area and entered the pavilion [for lunch], Jadeja turned suddenly and took steps towards Anderson in an aggressive and threatening manner," the ICC said.
All Level 2 breaches carry a fine of between 50-100% of a player's match fee and/or up to two suspension points. Two suspension points equates to a ban of one Test, or two one-day internationals.