EW.com said Lee is to film two performances with audiences and a third one without spectators during the course of a weekend this month.
The show's producers are financing the production, which is expected to air on cable television, EW.com said.
The musical is about a young black musician, raised in a church-going, middle-class Los Angeles neighborhood, who decides to embark on a journey to find "the real," entertainment news Web site said.
Lee's movies include "Mo' Better Blues," "She's Gotta Have It," "Jungle Fever," "Malcolm X" and "Inside Man."
"Passing Strange" won a Tony this year for best book for a musical and was nominated for six other Tonys.
Ray Liotta sues skin care company over use of likeness
NBC reportedly holds celebs hostage to Jimmy Fallon's show