Referee Manuel Graefe missed the incident, but German football officials reviewed the matter.
Senegal international Djilobodji, on loan from Chelsea, made the gesture towards Mainz winger Pablo de Blasis.
Werder have appealed in a bid to ensure Djilobodji, 27, can help them battle relegation from the Bundesliga.
They are one point above the drop zone with seven games left to play.
Djilobodji, who joined Bremen in January, faces a further one-game suspension after picking up his fifth yellow card against Mainz.
Werder Bremen defender Papy Djilobodji has been banned for two games after making a throat-slitting gesture during Saturday's 1-1 draw with Mainz.