The charge relates to an incident in the 86th minute of the game at the Hawthorns, when the Senegal defender appeared to shove West Brom's Darren Fletcher in the face at a set-piece.
Referee Craig Pawson did speak to both players at the time but the game's governing body have confirmed that the incident was not seen by any of the three match officials.
The incident was caught on video and highlighted on Match of the Day on Saturday night.
Djillobodji has until 6pm tomorrow to respond to the charge.
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The incident will be viewed by three former elite level officials, to determine whether a red card should have been issued. The decision must be unanimous for a ban to be issued.
Having been sent off against Hull City earlier this season, he would face a four game ban if found guilty, keeping him out of action until March and leaving Sunderland desperately short of defensive options.
Joleon Lescott is currently training at the club with a view to a possible short-term deal.