Larson, seen most recently in Free Fire, will play Victoria Woodhull, a suffragette nominated for President of the United States in 1872.
While Woodhull did not win the presidency, she helped in the fight to give women the vote - achieved some 40 years later.
The film, for Amazon Studios, will be written by Ben Kopit.
Lloyd Braun and Andrew Mittman will also produce Victoria Woodhull, according to Deadline Hollywood.
Larson, who won the best actress Oscar for Room, also appears in monster epic Kong: Skull Island.
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Oscar-winner Brie Larson is to star in - and produce - a film about the first female White House candidate.