Artistic director Dan Pengelly said
the Court offered its sincere and unreserved apologies for the distress caused by the casting decision
He said with the agreement and support of the original cast member, it was taking the necessary steps to recast the role.
The play runs until April 17 at the Court - and is being made into a TV series starring Nicole Kidman.
In a post on the theatre's Facebook page, it said: "We appreciate the courage of the artists and members of the community who have communicated with us over this issue, we offer our thanks for reaching out.
"We commit to putting in place measures to ensure this new cast member will be supported, and we are seeking guidance from experts in the trans community."