Parra, who has been replaced by Baptiste Serin, was recalled to the squad after not playing for his country since October, 2015 and not featuring under previous coach Guy Noves.
New coach Jacques Brunel will also have to cope with the absence of injured fullback Brice Dulin, who has been replaced by Hugo Bonneval.
France take on Ireland at the Stade de France on Feb. 3.
Les Bleus, who finished last year's Six Nations in third place, are still reeling from a dismal autumn campaign.
Brunel had called up the gritty Parra to boost the team's self-confidence but he will now have to turn to Maxime Machenaud or Serin.
They also lost Mathieu Bastareaud last week after the burly centre was handed a three-week ban for making a homophobic remark to a player during a Champions Cup game with his club Toulon.
(Reporting by Julien Pretot,; Editing by Ed Osmond)
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