Bellamy and Gary Neville have both received warnings from the Football Association following incidents in Sunday's highly-charged Manchester derby.
The FA launched an investigation after Manchester City striker Bellamy shoved his hand into the face of a fan who invaded the Old Trafford pitch.
Neville, a non-playing Manchester United substitute, was also investigated for his actions in celebrating the home side's winner by running down the touchline towards the City fans.
The FA have decided against charging either player with improper conduct.