The band will perform a stage version of their 2002 album Yoshimi Battles the Pink Robots, which has been directed by Des McAnuff.
The production runs from November 6 to December 16 at the La Jolla Playhouse in San Diego, California.
Describing the show, the producers stated: "Yoshimi is a young Japanese artist facing the battle of her life: the battle for her life. Adrift from her family and lover, Yoshimi journeys alone into a fantastical robot-world where she wages a war with fate.
"Will her will to survive be powerful enough to master the evil forces that threaten to destroy her?"
The show will also include music from other Flaming Lips albums including The Soft Bulletin and At War with the Mystics.
The musical was originally going to be written by The Social Network's Aaron Sorkin, but he later dropped out after he discovered the dialogue would be entirely in song.
The Flaming Lips recently broke a record for the most live shows played in 24 hours.
Watch the video for 'Yoshimi Battles the Pink Robots' below: