Barton had given Rangers an early lead on Monday before then getting involved in a tussle with Bradley Johnson, and appearing to headbutt the Norwich midfielder.
Initially play continued, before referee Neil Swarbrick consulted his assistant nearest to the incident and then produced a red card.
QPR said in a statement on their official website: "QPR have formally lodged an appeal to the Football Association following Joey Barton's sending off against Norwich City on Monday 2nd January."
The FA will also be seeking observations from QPR over comments from director Ruben Emir Gnanalingam.
Norwich went on to win Monday's game through goals from Anthony Pilkington and Steve Morison, to leave QPR just above the relegation zone.
In his post-match press conference, QPR manager Neil Warnock claimed he held little hope of lodging a successful appeal against what is set to be a three-match ban for violent conduct.
QPR must now present supporting evidence ahead of an independent disciplinary hearing, which will convene and make a decision ahead of the weekend's FA Cup third-round tie at MK Dons.
Television footage from the game initially proved inconclusive, with no real close-ups because of the position of cameras at the stadium.
What was clear from the long-range pictures was that Barton clashed with Norwich defender Zak Whitbread and then Johnson in the centre circle, ahead of directly squaring up to the Canaries midfielder.
Warnock branded Johnson a "disgrace" for his reaction, while Barton immediately took to Twitter to launch an impassioned defence of what he viewed as a "ridiculous decision", claiming the officials had been "conned".
Barton added on Twitter: "Why don't they copy rugby and cite incidents instead of taking a blind stab at decisions? There's too much money involved for guesswork.
"Respect the officials campaigns am all for it, think our officials get a hard time of it but respect is a 2 way thing. Hopefully it's rescinded and although it's frustrating for our club, justice will albeit far too late prevail."
It is understood that the FA have decided the post-match comments from manager Warnock do not warrant any further action.
However the club could face sanction over an apparent Twitter remark from director Emir Gnanalingam.
The message, which was swiftly deleted, is reported to have hit out at the referee being "biased and blind".
A fresh Twitter message has since appeared from Gnanalingam, a Malaysian businessman who joined the board in August following Tony Fernandes' takeover, saying simply: "EPL should consider video evidence for red cards. The 4th official is there and can communicate with ref immediately."
In September, the FA wrote to QPR owner Fernandes for Tweeting "this referee is blind" when Michael Oliver failed to award a penalty against Aston Villa despite a clear handball by defender Alan Hutton.
It is understood QPR will be contacted again in writing by the governing body for their observations over the latest comments.
Norwich midfielder Johnson, meanwhile, was pictured at the PDC World Darts Championship final on Monday night with a placard mocking the QPR captain. It read: "Barton, your breath stinks."
While Barton's red card captured the headlines, the defeat was a ninth defeat in the last 11 games for QPR.
Warnock is expected to further strengthen his squad during the January transfer window, having named on-loan Manchester United striker Federico Macheda among the substitutes on Monday, as the west London club look to pull clear of the bottom three.
QPR have allowed midfielder Jason Puncheon to return to Southampton following just two appearances in his loan spell.