Fugate, who wrote the Garry Marshall films Valentine's Day and New Year's Eve, will also direct the film, based on Martin's journey from growing up in West Virginia to being the first woman signed by Don King.
Christy, who was nicknamed The Coalminer's Daughter, was on the undercard of the infamous 1997 bout in which Mike Tyson bit the ear of Evander Holyfield.
She married her trainer Jim Martin, and when they first met in the training ring her broke her ribs in a bid to deter her from boxing.
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The film is a true story of inspirational boxer Christy Martin and her life.
This will be the first decidely dramatic role for Schumer, who has made a name for herself as a comedy actress in films like "Trainwreck", "Snatched", and "I Feel Pretty", which opens in the US this week.
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Christy also fought Laila Ali, the daughter of late boxing icon Muhammad Ali, in a high-profile 2003 bout in which Laila knocked her out. Spurred by Christy's romance with another female, Jim horrifically attacked his wife upon hearing the news that she planned to end their marriage. Her husband, on the other hand, was convicted and rightfully sent to jail. She would go on to testify in the 2012 trial that landed him behind bars for 25 years on a conviction of attempted second-degree murder with a firearm.
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