The Bayern Munich winger's participation at the tournament had long been in doubt due to the problem, which kept him out of France's warm-up games with Norway and Paraguay.
Ribery had hoped to be fit for Sunday's clash with Jamaica, but was withdrawn from the national squad by coach Didier Deschamps on Friday.
Lyon midfielder Clement Grenier has also been omitted due to a thigh problem, with Southampton's Morgan Schneiderlin and Montpellier playmaker Remy Cabella coming in as the replacements.
The absence of Ribery serves as a huge blow to France's prospects in Brazil, and the 31-year-old was understandably downbeat at the news.
"It is like a death in the soul that I am forced to leave the France team and give up on the World Cup," he told the French Football Federation's (FFF) website.
"I always hoped to be able to play against Jamaica 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."
