The Manchester City captain was sent off just 10 minutes into Saturday's 2-0 Premier League win at Hull City for a professional foul on Nikica Jelavic.
Kompany reacted to his dismissal at the KC Stadium with a gesture to the fourth official and then kicked a wall as he went down the tunnel to the dressing room as his frustration got the better of him.
The FA have considered the Belgium captain's explanation for his actions following his red card and confirmed to Perform that they have opted to take no further action, so he will only sit out Saturday's top-flight clash with relegation-threatened Fulham.
The influential centre-back will then be clear to return for City's crunch clash with champions United at Old Trafford next Tuesday as Manuel Pellegrini's men strive to stay in the title race.
Hull forward George Boyd was earlier charged on Tuesday by the FA for allegedly spitting at City goalkeeper Joe Hart.
