"Arsenal and Tottenham Hotspur have been charged following their game. It is alleged that in the 32nd minute, they failed to ensure that their players conducted themselves in an orderly fashion," the FA said in a statement.
The clubs have until 1800GMT on Thursday to respond.
Gabon striker Pierre-Emerick Aubameyang's brace and strikes from Alexandre Lacazette and Lucas Torreira helped Arsenal cancel out goals from Dier and Harry Kane.
Arsenal, who have 30 points from 14 games, leapfrogged Tottenham to fourth place in the standings on goal difference.
Up next for Arsenal is a trip to Manchester United on Wednesday while Tottenham host managerless Southampton.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Christian Radnedge)
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