The production will now open May 9 (in a change from the previously announced May 8), following previews that begin on May 1. Murray joins a cast that includes the previously announced Lindsay Duncan, Matt Smith, Catherine Steadman and Julian Wadham.
The actress will play Mia, daughter of Duncan's character Martha and brother to Smith's character Henry in the play that revolves around a family in freefall. The school-age siblings have to become parents to their mother.
Murray can also be seen in playwright/director Martin McDonagh's film "In Bruges."
That Face is booking at the Duke of York's Theatre to July 5. For tickets call the box office at 0870 060 1483 or visit www.thatface.co.uk.