"Tinker Tailor Soldier Spy" and "Let the Right One In" helmer, Tomas Alfredson, will direct the film, said The Hollywood Reporter.
The Universal and Working Title-film centres on a detective named Harry Hole, who investigates the disappearance of a young boy's mother.
All that is left of her is the pink scarf her son gave her for Christmas, which is now wrapped around a snowman that mysteriously appeared in the front yard.
As he digs deeper into the case, he comes to realise he may be tracking Norway's first official serial killer.
The series follows the Norwegian detective, who is known for his brilliance and his unorthodox methods, as he solves crimes around Oslo.
Filmmaker Martin Scorsese was attached to direct the film in 2011.
Fassbender, 38, will be next seen in "MacBeth", Fox's "X-Men: Apocalypse" and video game adaptation "Assassin's Creed".
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