Giroud had just been sent off during the clash at The Emirates, for headbutting R's defender Nedum Onuoha during the first half.
In response Ferdinand grabbed Giroud by the back of the neck, in an action unseen by the referee.
Giroud faces a three game ban for his sending off, during a busy period of games in which Arsenal can ill-afford such a needless suspension.
The French international will miss matches with West Ham, Southampton, and Hull City in the FA Cup.
Arsene Wenger had little sympathy for his player, stating: "It was was a deserved red card, Olivier didn't control himself. It completely changed the dynamic of the game."
Ferdinand is a well known foe to Arsenal from his decade with Manchester United, but was left smarting at the final whistle with the Gunners defeating QPR 2-1, but he later apologised on Twitter.
Disappointing result..could have nicked a draw towards the end with a bit of luck! Ps..apologies for feeling the hairs on Girouds neck back!— Rio Ferdinand (@rioferdy5) December 26, 2014