The Lyon midfielder was part of France coach Didier Deschamps' 23-man squad for the marquee tournament that starts in Brazil next week.
However, Grenier pulled up in training with a groin injury on Thursday - having been plagued by a similar issue at the back end of the Ligue 1 season - and was subsequently ruled out of the tournament.
Writing on his official Twitter account, Grenier said: "Thank you for all your messages of support. They are going straight to the heart.
"This is a difficult time but I will come back stronger."
Grenier's injury represented part of a double blow for Deschamps, after it was announced talisman Franck Ribery would also miss the World Cup.
The Bayern Munich winger had hoped to recover from a back injury in time to feature, but had to leave training on Friday after suffering pain in the warm-up.
Montpellier's Remy Cabella and Southampton's Morgan Schneiderlin have been called up as replacements.
France begin their World Cup campaign with a Group E encounter against Honduras on June 15.
