The German-born singer is known as the original "femme fatale|" of art-rock in the Sixties, and appeared on the seminal 1967 album The Velvet Underground and Nico.
However, The Nico Project will focus more on the album that followed: Nico's bleak solo record The Marble Index.
Peake, known for her roles in Silk, Black Mirror and Three Girls, said she was attracted by Nico's "dark side" and wanted to know "where does that come from?"
"I remember first listening to The Marble Index in my late teens in a dark room and I felt very uneasy about it," she told the BBC.
"It takes you to uncomfortable places, but it's beautiful at the same time. And I'm just fascinated with people who allow that to really seep out of them, to express that and go to those places that most of us try to avoid."
The project is being produced by an all-female creative team led by director Sarah Frankcom. It will be staged in July at the Manchester International Festival.
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