The Bayern Munich ace had been struggling with a back problem for the past few weeks but had been expected to feature in Les Bleus' final warm-up fixture against Jamaica.
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"It is soul-destroying being forced to leave the France national team and forego the World Cup," the 31-year-old winger told the French Football Federation's official website.
"I always hoped to be in the attack for the Jamaica game, particularly after noting encouraging signs in recent days.
"But extensive tests I underwent on Friday morning revealed my back pain. An MRI at Rambouillet hospital only confirmed my inability to train and play normally.
"Given these circumstances and despite the care provided by the medical staff, which I sincerely thank them for, my withdrawal was inevitable.
"I now leave my team-mates with a heavy heart, but I know they will do the maximum for the blue shirt and go as far as possible in the competition.
"I know I can trust them. I am now their biggest supporter."
Ribery's withdrawal was not the only blow France suffered on Friday, as Clement Grenier was also forced to pull out. The pair have been replaced in the squad by Remy Cabella and Morgan Schneiderlin.