A back problem saw the Bayern Munich star withdrawn from the squad on the same day as Lyon midfielder Clement Grenier, who has a thigh injury. Montpellier's Remy Cabella and Southampton's Morgan Schneiderlin will replace the pair.
Ribery said on the French Football Federation's official website: "It is like a death in the soul that I am forced to leave the France team and give up on the World Cup.
"I always hoped to be able to play against Jamaica (in this Sunday's final warm-up friendly) but when I pushed it physically on Friday morning it aggravated my back pain.
"The MRI scan confirmed those feelings and therefore my inability to train and play normally.
"In these conditions and despite the efforts of the medical staff, who I thank sincerely, my absence was inevitable."
Coach Didier Deschamps said in a press conference screened on the French Football Federation's official website: "It's a sad day.
" You have on one side two players who are happy to be joining us, and two others who are very sad."
Ribery had been following an individual training programme to overcome a back problem which has sidelined him since Bayern's DFB-Pokal final on May 17.
He had hoped to rejoin the full squad on Friday but Deschamps said: "We increased the intensity of his work but this morning, before he could join the collective training, he stopped dead on a movement with a sharp pain.
"As of today, everything leads us to believe that he will be unable to train for several weeks, and still less able to play."
Regarding Grenier, he added: "He had a groin problem in the second half of the season but had an operation and returned for the last match.
"He played in the (warm-up) matches against Norway and Paraguay and o n Wednesday he trained as normal, Thursday morning as well, but on Thursday afternoon in the game he felt a violent pain in his right adductor and had to leave the session.
"He had an MRI scan, which unfortunately showed a tear in the adductor meaning an absence of several weeks."
On replacements Schneiderlin and Cabella, he said: "These two players were on the reserve list and they are similar to the two players who left us.
"It is not a cut-and-paste, but Morgan can link up play like Grenier and Cabella is closest to the profile of Franck Ribery."
Deschamps had previously been forced to call up St Etienne's Stephane Ruffier to replace injured Marseille goalkeeper Steve Mandanda.
The former OM coach admitted Ribery's absence, in particular, is a major setback but vowed not to lose heart ahead of the tournament.
He said: "We know what Franck is capable of. But I have other players.
"Part of my job is to anticipate things and try out different options. There are lots of possibilities. (Antoine) Griezmann has done some good things.
"With Franck Ribery at 100 per cent, we are better. But we have to be ambitious and we will continue to be."
Ribery added: "I depart from my team-mates with a heavy heart but I know they will do all they can for the blue jersey and go as far as possible in the competition. I will be their number one supporter."
Real Sociedad star Griezmann, Cabella and OM's Mathieu Valbuena will provide the wide options for Deschamps.
For Ribery, it marks the end of his World Cup career if a recent interview he gave to radio station RTL is to be believed.
"It will be my last World Cup," he said on May 21. "We have to go there to try to win the World Cup."
The 31-year-old made his international breakthrough by helping Les Bleus to the 2006 final in Germany, where they lost on penalties to Italy, but was also part of the wretched 2010 campaign in South Africa which ended in mutiny against then coach Raymond Domenech .
This summer's competition would have been a first World Cup for Grenier, who has won five caps for Les Bleus since making his debut against Uruguay last year.
The 23-year-old made 36 appearances for Lyon last season, recording six goals and five assists. He turned down a move to Newcastle in January as the Magpies sought a replacement for departed France star Yohan Cabaye.
Both he and Ribery appeared on the official squad photo published earlier on Friday by the FFF but Cabella will now take Ribery's number seven shirt, with Schneiderlin taking over from Grenier at number 22.
Cabella made his senior France debut as a 79th-minute substitute in last Tuesday's 4-0 friendly win over Norway, after 17 caps and four goals at under-21 level.
The uncapped Schneiderlin has spent six years at Southampton and has played in the top three divisions of the English league.
He began his career with Strasbourg and has won three under-21 caps and five for the under-20 side, scoring once at each level.
- Sports & Recreation
- Morgan Schneiderlin
- French Football Federation
- Remy Cabella
- Didier Deschamps