Gina Lipinski, who assisted Flimm in staging the production when it premiered at the Metropolitan Opera, will fill in for him, the Lyric announced.
According to the company, Flimm withdrew because of an "unexpected administrative emergency" at the Salzburg Festival, where he is director of theater and will become artistic director in 2006.
Lipsinki is a staff member at the Metropolitan Opera, and has directed productions at San Francisco Opera and Cleveland Opera.
Fidelio runs from January 18 through February 21, and stars Karita Mattila as Leonora. Christoph von Dohnšnyi conducts.