The Egyptian was sent off in the second half of the league leaders' shock 2-1 loss on Wednesday for elbowing Ankaragucu midfielder Ibrahim Akdag.
The 23-year-old will have to sit out one match and pay a fine of 13,000 liras ($1,725) for unsportsmanlike behavior, the Turkish Football Federation (TFF) said in a statement.
Galatasaray's appeal against the ban was rejected by the disciplinary committee, according to the TFF. Mohamed will miss Sunday's Super Lig fixture against Demir Grup Sivasspor.
