The cast will also feature the previously announced Emmy Award winners Richard Thomas and James Spader.
Race, by the author of American Buffalo, Glengarry Glen Ross, Speed-the-Plow, November and The Cryptogram, will officially open on Broadway Dec. 6.
Mamet will also direct.
The design team will include set designer Santo Loquasto, lighting designer Brian MacDevitt and costume designer Paul Tazewell.
Washington's screen credits also include "Life Is Hot in Cracktown," "Lakeview Terrace," "Woman in Burka," "Put It in a Book" "I Think I Love My Wife," "The Dead Girl," "Little Man," "Boston Legal," "Wait," "Sexual Life," "Against the Ropes," "The Human Stain" and "Bad Company," among others. Race will mark her Broadway debut.
The New York Times first reported the Kerry Washington casting.
The Barrymore, which was the recent home of the much-in-the-news revival of Mamet's Speed-the-Plow, is located at 243 West 47th Street.