The screening will be thrown at the Newseum. Bigelow and her screenwriting partner Mark Boal will attend the event to discuss the movie after the showing, reported Ace Showbiz.
The promo event will see a number of politicians, members of the executive branch, opinion makers and Washington journalists.
Sony pictures initially wanted to host the Washington premiere on December 4, just before the film hits limited theaters in Los Angeles in New York on December 19.
However, the studio finally decided to make it a premiere to anticipate the nationwide expansion of the movie instead.
"Zero Dark Thirty" follows the footsteps of a number of political films which threw a Washington premiere in the past.
In 2001, Ridley Scott's "Black Hawk Down" was screened in the capital, followed by Phil Alden Robinson's "Sum of All Fears" a year later.
Last month, Steven Spielberg's "Lincoln" also held a President Obama-hosted premiere in the nation's capital.