Vieira left out for World Cup play-off
Midfielder Vieira, who has won 107 caps but is struggling, at 33, to recapture his best form and rarely starts for his Inter Milan club, was not on the 24-man list named on Thursday by Raymond Domenech.
The France coach picked two uncapped players in Girondins Bordeaux goalkeeper Cedric Carrasso and Olympique Lyon defender Aly Cissokho.
Domenech will also have to make do without Franck Ribery, sidelined with a niggling knee injury, but still has plenty of talent in his squad with the likes of playmaker Yoann Gourcuff and forwards Thierry Henry and Karim Benzema.
Lyon keeper Hugo Lloris, who was outstanding in his side's 1-1 Champions League draw with Liverpool on Wednesday, is expected to play in goal.
France visit Ireland on November 14 at Croke Park before welcoming them to the Stade de France four days later. The winners of the tie will play in next year's finals in South Africa.
"To have two games like these to play is important for a whole generation," Domenech, who has faced criticism in France for years and knows his job will be on the line, told a news conference.
"We need total support from the public," added the France coach, whose team have been jeered by their own fans in recent outings.
Asked whether the fact Ireland were coached by Italian Giovanni Trapattoni boosted his motivation, Domenech, whose team lost to Italy in the 2006 World Cup final, said: "No, this is France against Ireland and the coaches don't play the matches.
"This is not a boxing fight, this is not a Frenchman against an Italian, just two coaches who want their team to qualify," he added.
Goalkeepers: Cedric Carrasso (Girondins Bordeaux), Hugo Lloris (Olympique Lyon), Steve Mandanda (Olympique Marseille)
Defenders: Eric Abidal (Barcelona), Aly Cissokho (Olympique Lyon), Patrice Evra (Manchester United), Julien Escude (Sevilla), Rod Fanni (Stade Rennes), William Gallas (Arsenal), Bacary Sagna (Arsenal), Sebastien Squillaci (Sevilla)
Midfielders: Abou Diaby (Arsenal), Alou Diarra (Girondins Bordeaux), Lassana Diarra (Real Madrid), Yoann Gourcuff (Girondins Bordeaux), Moussa Sissoko (Toulouse), Jeremy Toulalan (Olympique Lyon)
Forwards: Nicolas Anelka (Chelsea), Karim Benzema (Real Madrid), Andre-Pierre Gignac (Toulouse), Sidney Govou (Olympique Lyon), Thierry Henry (Barcelona), Florent Malouda (Chelsea), Loic Remy (Nice).