The clash, which occurred as the players left the field at lunch on the second day, saw Jadeja charged with a level two misconduct charge for allegedly approaching Anderson in a threatening manner.
Anderson was charged with a level three offense for having "abused and pushed" his opponent.
Match referee David Boon found Jadeja not guilty of the offence for which he had been charged, but felt his conduct was contrary to the spirit of the game.
"While I was in no doubt that confrontation did occur, and that such conduct was not in the spirit of the game and should not have taken place, I was not comfortably satisfied that this was a level 2 offence," Boon, the former Australia batsman, said in a statement on Friday.
"Therefore, in exercising my discretion under Article 7.6.5 of the Code and having heard all the evidence, I was comfortably satisfied that Mr Jadeja had committed a level 1 offence under Article 2.1.8 of the Code."
Anderson's hearing will be held on Aug. 1, the day after the third test at Southampton is scheduled to finish, where he faces a possible four-test ban if he found guilty.
India lead the five-match series 1-0.