Will Eno's new play begins performances at Broadway's Lyceum Theatre on March 13.
Gyllenhaal was announced to star in the leading role, but has since departed.
The organization will also showcase Tom Stoppard's Indian Ink and The Real Thing next season.
Emily Skeggs will take over the role of Medium Alison.
Sam Gold directs the revival of Tom Stoppard's Tony-winning drama in October 2014.