The former Tottenham Hotspur player received the suspension as a result of the red card that he was handed during Saturday's match against Huddersfield Town.
Having been fouled by Keith Southern, O'Hara reacted by pushing the Huddersfield midfielder and was consequently dismissed.
While they accepted the red card, Wolves felt that the three-game penalty was harsh and lodged an appeal with the Football Association yesterday afternoon.
However, having considered the incident, the governing body have decided that the original punishment should stand. The 26-year-old will now miss encounters against Hull City, Charlton Athletic and Burnley.