Nkunku suffered a leg injury in training on Tuesday during a challenge with Real Madrid midfielder Eduardo Camavinga.
The 25-year-old had to be helped off the field by the France medical team.
"Injured in training, Christopher Nkunku must give up participating in the World Cup. The whole group shares Christopher's sadness and wishes him a speedy recovery," wrote the national team in a statement.
Nkunku is one of the most in-form French players, having struck 12 goals in 15 Bundesliga games this season.
He was voted the Bundesliga's player of the season last term after scoring 20 goals and providing 13 assists in 34 matches.
France have already been robbed off the services of three members of their victorious 2018 World Cup campaign after N'golo Kante, Paul Pogba and Presnel Kimpembe succumbed to injury while they are also sweating on the fitness of Karim Benzema and Raphael Varane.
France manager Didier Deschamps is yet to call up a replacement for Nkunku.
France are in the same group with Australia, Denmark and Tunisia.
