The historical figure is best known for fearlessly leading the French in battle against English troops in the Hundred Years’ War.
London theater owners say the play, I, Joan – which charts the life of the French patron saint – will “offer the possibility of another perspective” when it arrives later this month.
The lead role will be played by Isobel Thom, who also uses the pronoun “they/them”.
“Throughout the centuries, Joan has been a cultural icon depicted in countless plays, books, films, and more,” said Michelle Terry, artistic director of The Globe.
“History has provided countless and wonderful examples of Joan being portrayed as a woman. This production is only offering the possibility of another point of view.
However, people took to social media to express their anger over the move.
Sophie Walker tweeted: “When I was a little girl, Joan of Arc presented exciting possibilities about what a young girl could do to a mass of men. Rewriting her as not a woman and calling it Presenting as progress is a huge disappointment.”
Journalist Alison Pearson wrote: “When I was a kid, I had a book about inspiring women through history. Joan of Arc was one. That book and those amazing women meant a lot to a timid little girl. @ How dare you cancel The_Globe, the inspirational women of history.”
Despite the uproar, many people supported the decision.
One fan tweeted: “I absolutely love the idea! Writers and scholars have spoken of Joan as a gender-conforming person who might have identified as trans or non-binary, Lived for decades today. I mean, the formal reason for Joan was her emphasis on cross-dressing.”
And radio presenter Natasha Devon posted: “You know one of the many productions you can see where Joan of Arc isn’t nonbinary, or Anne Boleyn isn’t played by a black woman, right?”
Ms Terry defended the creation of the Globe, saying: “Theatres produce plays, and in plays, anything is possible.
“Shakespeare did not write historically accurate plays. He took figures from the past to ask questions about the world around him.
“Shakespeare was not afraid of discomfort, and neither did the globe.”
A statement on The Globe’s website confirmed that it was “committed to becoming an inclusive and diverse organization” that was ready to make the “necessary changes”.
“Our aim is to create a culture and environment in which everyone’s experience at Shakespeare’s Globe is equal, inclusive and equal,” it said.