The ban relates to a stamp on young winger Adnan Januzaj in Fulham's 3-1 defeat to Manchester United on Saturday which was not seen by referee Lee Probert or his assistants.
The German full-back apologised for the incident via his official Twitter account on Tuesday, adding: "I will accept the consequences of my actions, and hope to put it behind me when I return."
Earlier in the day, it was reported Fulham were delaying accepting the charge as they sought clarification on certain points of the newly-instigated rules that govern when action can be taken.
However, Riether accepted the charge after becoming the first player to be punished under the Retrospective Action Scheme.
An FA panel of three former referees - Steve Dunn, Eddie Wolstenholme and Alan Wiley - were unanimous in their decision that the incident represented an act of violent conduct. The panel made the ruling on what they believe the official would have done had he seen it.
Last month, FA chairman Greg Dyke revealed his concern about inadequate disciplinary procedures against players after Chelsea striker Fernando Torres appeared to scratch Tottenham defender Jan Vertonghen in September.
"When millions of fans watching on TV can see an incident like this and the FA does not take action it is understandably baffling to everybody and has to be addressed," Dyke told the Leaders in Football conference.
"For the FA's disciplinary department to find itself in a position where it is not able to take action against an obvious scratch just can't be right.
"What this means is, despite the rules being changed in the summer, they clearly weren't changed enough.
"As FA chairman I don't like to be in a position where I cannot explain the rules when action should be taken when something is pretty obvious."