United manager, Jose Mourinho, will also face no disciplinary action for his comments before the game.
The FA reached the verdict, after studying the written submissions provided by both clubs after the December 10 game, which City won 2-1.
“Following a review of the evidence provided by the clubs and independent eyewitnesses The FA will be taking no formal action,” an FA statement read.
With Greater Manchester Police also choosing not to take the matter further, it now appears that the authorities regard the incident as closed.
United and City meet again in the Premier League at the Etihad Stadium on April 7.