Ferdinand tripped the striker before pushing him in the back during the last few minutess of the clash at Old Trafford.
Having reviewed video footage of the incident, the Football Association has decided not to take the matter further.
Manchester United let a two-goal lead slip as Chelsea turned up the heat and second-half goals from Eden Hazard and Ramires earned Chelsea a replay at Stamford Bridge.
The confirmation means Ferdinand will be free to play in the quarter-final.
Goals from Javier Hernandez and Wayne Rooney inside the first 11 minutes put United apparently on the brink of a semi-final berth.
But a complacent United allowed the Blues hit back in the second half and Eden Hazard halved the deficit just before the hour, with Ramires levelling in the 68th minute. Chelsea were unlucky not to have won the tie as Juan Mata had a last minute shot saved.
The winners will face Manchester City in the last four but a suitable date to hold the replay has yet to be settled on.