The Serbian international was found guilty of violent conduct on Thursday following an incident in the 2-1 Premier League victory over Wigan Athletic at Stamford Bridge on Saturday, the FA said in a statement.
Television replays showed Ivanovic lashing out at Wigan's Shaun Maloney in an off-the-ball incident unseen by the match officials and he was charged retrospectively.
Ivanovic appealed against the charge but it was dismissed by the FA.
The defender will also miss Premier League games against Arsenal and Queens Park Rangers but is available for both legs of the Champions League semi-final against Barcelona.
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