The series, based on the rivalry between Bette Davis and Joan Crawford, featured Catherine Zeta-Jones as de Havilland.
The veteran star, who turned 101 today, is suing the network and Murphy's production company over what she contends is an unauthorised and inaccurate portrayal of her, reported Entertainment Weekly.
Her lawyers say that despite being the only living person who was depicted as a major character, she was not consulted about her portrayal on the show.
"Further, the FX series puts words in the mouth of Miss de Havilland which are inaccurate and contrary to the reputation she has built over an 80-year professional life, specifically refusing to engage in gossip mongering about other actors in order to generate media attention for herself."
De Havilland, who lives in Paris, filed the complaint in Los Angeles Superior Court yesterday.