A back problem meant he was ruled out of the tournament on the same day as Clement Grenier, the Lyon midfielder, who has a thigh injury. Montpellier's Remy Cabella and Southampton's Morgan Schneiderlin will replace the pair.
Ribery said: "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.
"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."
The 31-year-old had been following an individual training programme since he was injured in Bayern's DFB-Pokal final victory over Borussia Dortmund on May 17. However, he was unable to recover in time.
Didier Deschamps, the France coach, said: "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. We increased the intensity of [Ribery's] 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. We know what Franck is capable of. With Franck Ribery at 100%, we are better. But I have other players. There are lots of possibilities. [Antoine] Griezmann has done some good things."
Deschamps had previously been forced to call up St Etienne's Stephane Ruffier in place of injured Marseille goalkeeper Steve Mandanda. Referring to his latest 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."
Cabella made his senior France debut as a 79th-minute substitute in last Tuesday's 4-0 friendly win over Norway, while Schneiderlin has yet to appear at full international level.