The 28-year-old Senegalese was involved in an 86th-minute incident with West Brom's Darren Fletcher and although it was missed by match officials it was caught on video.
Djilobodji had denied the charge, prompting an Independent Regulatory Commission hearing.
The four-game ban, rather than the standard three, was imposed because it was his second dismissal this season.
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Bottom club Sunderland will be without Djilobodji until March 5, meaning he will miss league games against Tottenham Hotspur, Crystal Palace, Southampton and Everton.
(Reporting by Martyn Herman, editing by Ed Osmond)
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