Ferdinand appeared to trip the striker before pushing him in the back during the closing stages of the clash at Old Trafford.
But having reviewed video footage of the incident, the Football Association has decided not to take the matter further.
United let a two-goal lead slip as 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 replay after the teams drew 2-2 at Old Trafford on Sunday.
Goals from Javier Hernandez and Wayne Rooney inside the first 11 minutes put United apparently on the brink of a semi-final berth.
But 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.
The winners will face Manchester City in the last four but a suitable date to hold the replay has yet to be settled on.
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