The feisty encounter produced 12 yellow cards as well as two mass brawls, in which both players and coaches were involved, as Chelsea fought back from two goals down to draw 2-2, a result which handed the title to Leicester
Dembele appeared to claw his fingers down Diego Costa's face during a skirmish at the end of the first half
The Football Association confirmed a disciplinary case had now been opened, which in Dembele's case could lead to an extended ban if proven
A statement read: "Both Chelsea and Tottenham Hotspur have been charged for three breaches of FA Rule E20 for failing to control their players and/or officials
It follows incidents which occurred in the 45th and 87th minutes and also at the end of the game at Stamford Bridge on Monday night [2 May 2016]
"Both clubs have until 6pm on Monday 9 May 2016 to respond to their charge.
"Meanwhile, Mousa Dembélé has been charged for an alleged act of violent conduct which was not seen by the match officials but caught on video during the same game.
"The Tottenham Hotspur midfielder was involved in an incident with Chelsea's Diego Costa near the end of the first half.
"Further, it is alleged the player's behaviour constituted violent conduct in circumstances where the standard punishment of three matches that would otherwise apply is clearly insufficient.
"The player has until 6pm on Thursday 5 May 2016 to respond to the charge."
Source: PA