The 21-year-old Italian will already serve a three-match ban following his red card at the end of the encounter, but it was expected that additional punishment would follow for his knee-high challenge on Song.
An FA statement read: "Retrospective action in relation to the incident involving Mario Balotelli of Manchester City and Alex Song of Arsenal, which occurred in the 20th minute of Sunday's game, will not be taken.
"Where at least one of the officials has seen the coming together of players retrospective action is not taken, regardless of whether they have seen the full extent of the challenge. Retrospective action can only be taken in scenarios where none of the match officials saw the players coming together.
"The normal scenarios in which retrospective action is taken are for 'off-the-ball' incidents. Retrospective action was introduced for off-the-ball incidents where there was no contest for possession and could not be deemed to be re-refereeing an incident."
Balotelli has received three red cards this season.