The Australia international caught West Ham's Diafra Sakho with his arm in an off-the-ball incident during the Premier League match at Upton Park.
Referee Mike Dean did not see the incident, but it was caught on video.
An FA statement explained the duration of the suspension: "The player's suspension consists of three matches for violent conduct with an additional one match as he has previously been dismissed this season."
Alan Pardew had defended his player, suggesting he was the victim of "trial by media".
However, Jedinak will now miss the matches against Southampton, QPR, Stoke City and Manchester City.
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