Lloyd, best-known for her acclaimed portrayal of the young Cynthia Payne in Wish You Were Here, was due to open on Monday in the George Bernard Shaw play at the Theatre Royal, Windsor.
The 26-year-old was to have starred as Eliza Doolittle alongside Michael Elphick and Roy Marsden.
The production is due to transfer to the Albery Theatre in the West End on 22 July, but now it will be without its star.
Lloyd's London-based agent, Ben Jones, said: "Yes, it is true she has pulled out, but I cannot say any more."
A statement from the play's publicist was expected later.
Shaw's play centres on Professor Higgins' wager with Colonel Pickering that he can transform a common Covent Garden flower girl into a lady fit to be presented at Court.
It was adapted for the screen and became a hugely successful film, My Fair Lady, starring Rex Harrison and Audrey Hepburn.