The new version of the celebrated social drama was adapted by Christopher Shinn and will be directed by Ian Rickson.
Preview performances at the American Airlines Theatre are to begin Jan. 6 with an opening night planned for Jan. 25. The production is to be a limited engagement.
This marks Parker's return to Broadway following her 2004 Tony-nominated performance in Craig Lucas' "Reckless." She had won a Tony Award for her work in "Proof."
Additional cast members and the design team for "Hedda" will be announced shortly, the Roundabout said.
Parker is starring on the Showtime series "Weeds" and has been seen in the films "Fried Green Tomatoes," "Mr. Wonderful," "Boys on the Side," "Red Dragon" and "The Assassination of Jesse James."