The German FA (DFB) said on Tuesday the suspension was for unsportsmanlike conduct after the Senegal international ran his finger across his throat in the direction of Mainz player Pablo De Blasis after they had tussled for the ball.
The DFB added that the ban would take effect after Djilobodji, 27, has served a one-game suspension for picking up his fifth yellow card of the season in the match against Mainz.
Chelsea signed Djilobodji from Nantes on a four-year contract on Sept. 1 for a fee put at 2.7 million pounds by British media but went out on loan in January.
Werder Bremen, who are one point above the relegation zone with seven games left, have decided to appeal the decision.
The DFB said Djilobodji's suspension was handed out in accordance with their decision in 2009 regarding Deniz Naki after the St Pauli forward made a similar gesture to Hansa Rostock fans in a league match and got a similar ban.
"We maintain that the ruling of a three-match ban is unjustifiable," Werder's chief executive Thomas Eichin was quoted as saying on the club's website (www.werder.de).
"Above all, we believe that, under the circumstances, the severity and the wrongdoing in this case was less than that of the Deniz Naki case," he added.
(Writing by Ken Ferris; Editing by Greg Stutchbury)
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