Variety reports that Mamet will also pen the film's script based on the famed diary and the original Albert Hackett-Frances Goodrich play.
Disney recently acquired the rights to the film, which will be produced by Andrew Braunsberg ("Being There") and writer-director Mamet.
The original 1959 "Anne Frank" film, also written by Hackett and Goodrich, won three Academy Awards.
No casting or timetable has been announced for the new version.
A founder of the Atlantic Theater Company, David Mamet's principal works include The Duck Variations, Sexual Perversity in Chicago, American Buffalo, Glengarry Glen Ross (Pulitzer Prize), Boston Marriage, Edmond, Oleanna, Speed-the-Plow and The Cryptogram (Obie Award). He adapted The Voysey Inheritance for the Atlantic and was also represented on Broadway with the political comedy November.
Last season Broadway offered revivals of Mamet's American Buffalo and the much-in-the-news Speed-the-Plow.
His new play Race will begin previews Nov. 16 at Broadway's Ethel Barrymore Theatre with an official opening scheduled for Dec. 6. The season will also feature the first-ever Broadway production of David Mamet's Oleanna — starring Bill Pullman and Julia Stiles — which begins previews Sept. 29 toward an Oct. 11 opening at The Golden Theatre.