No reason was given for Franco's departure, but EW.com noted how busy the actor and painter has been in recent years.
In addition to his film work, Franco also served as co-host of this year's Academy Awards show, guest starred on the daytime soap "General Hospital" and is pursuing degrees at numerous universities.
Director David Cromer told the New York Times the production of "Sweet Bird of Youth" may be part of the 2011-12 theater season, however, nothing has been confirmed at this time.
Nicole Kidman was previously announced as the play's female lead.
Franco's film credits include "Rise of the Planet of the Apes," "127 Hours," "Milk," "Howl" and "Spider-Man."