The exhibit is being organised by MoMA curator-at-large Klaus Biesenbach, and will include biographical and fictitious text written by Bjork and poet Sjon, reported ABC News.
A statement on Bjork's website has promised that "costumes, performances, instruments and more" from throughout the singer's 20-year solo career will be on display.
The Museum of Modern Art is also adding the application version of Bjork's 2011 album Biophilia to its digital design collection in a first for the institution.
Bjork has described that LP as being "folk music of our time", rather than rock or pop in style.