Coach Didier Deschamps also said that attacking midfielder Clement Grenier was out of the finals in Brazil with a groin problem as Les Bleus suffered their third injury since the 23-man squad was unveiled. Second-choice goalkeeper Steve Mandanda also pulled out.
"This morning before the collective training session ... he had to stop, the pain was too strong," Deschamps told a news conference.
"We have made checks in the beginning of the afternoon, checks that confirmed the situation has aggravated and he is today not capable of training for a few weeks, let alone play a game."
The replacements have to be validated by world governing body FIFA as they are made after the 23-man squad submission deadline, which was on June 2.
"We will hand over those two files and they will take the time they need to reply," said Deschamps.
"They are the first, Franck or Clement, to be very sad. Franck had problems but everything was going in the right direction until his situation suddenly aggravated."
Ribery was instrumental in France's qualifying campaign, scoring five goals and creating several chances for his team mates.
He has been suffering from lower back pains for weeks, playing his last game in the German Cup final on May 17 when he came as a substitute for Bayern Munich but could not finish the match.
Without him, Les Bleus beat Norway 4-0 and drew 1-1 against Paraguay in their two World Cup warm-up games.
Both put in solid displays with Griezmann scoring the goal against Paraguay.
Deschamps probably wanted to avoid the mistakes his predecessors made when they took major players to tournaments with injuries hoping they would return to fitness during the competition.
In 2002, France coach Roger Lemerre took Zinedine Zidane to the World Cup after the playmaker had injured his thigh in their last warm-up game against South Korea. Zidane could only play in the final group game against Denmark and made no impact as Les Bleus crashed out in the first round.
At the 2008 European Championship, coach Raymond Domenech included the injured Patrick Vieira in his squad but he never played as France were also eliminated in the group stage.
With Ribery out, Deschamps could have called up Manchester City's Samir Nasri but having made clear he had not picked him in the first place because of his behaviour off the pitch, he overlooked him again.
France take on Jamaica in Lille on Sunday in their last warm-up game before the World Cup.
Defenders: Mathieu Debuchy (Newcastle United), Lucas Digne (Paris St Germain) Patrice Evra (Manchester United), Laurent Koscielny (Arsenal), Eliaquim Mangala (Porto), Bacary Sagna (Arsenal), Mamadou Sakho (Liverpool), Raphael Varane (Real Madrid)
Midfielders: Yohan Cabaye (Paris St Germain), Blaise Matuidi (Paris St Germain), Rio Mavuba (Lille), Paul Pogba (Juventus), Moussa Sissoko (Newcastle United), Mathieu Valbuena (Olympique Marseille), Remy Cabella (Montpellier), Morgan Schneiderlin (Southampton)
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- Newcastle United
- Remy Cabella