Barton was given his marching orders in Monday's 2-1 defeat at Loftus Road following a tussle with Norwich's Bradley Johnson.
Barton and manager Neil Warnock courted controversy by claiming match officials had been duped into giving the QPR midfielder a red card, and on Tuesday confirmed they would appeal the decision.
However the FA said in a statement the appeal had been dismissed and Barton would now serve a three-match suspension, effective immediately.
"An Independent Regulatory Commission has today dismissed a claim of wrongful dismissal from Queens Park Rangers midfielder Joey Barton following his red card for violent conduct in the QPR v Norwich City game on 2 January 2012," the FA said.
"Barton will serve a three-match suspension with immediate effect."
Source: PA
Source: PA