Following the immense success of The Legend of Zelda: Ocarina of Time, Nintendo's Shigeru Miyamoto had intended to develop the Master Quest version of the game in just a year's time. Instead, current Zelda producer Eiji Aonuma proposed that a new game be created. Given the planned one year development period, Miyamoto challenged Aonuma "If you can create a new Zelda in that time, then please try.” With a tough deadline in mind, Aonuma broke ground on what would become Majora's Mask.
Given the insanely tight schedule, Aonuma and the rest of the Zelda team brainstormed ideas on how they could create a full Zelda experience with smaller volume. Longtime Nintendo developer Yoshiaki Koizumi brought up the movie Run Lola Run, which stars a girl who re-lives the same time periods multiple times. Applying this idea to the game, the Zelda team initially set out to create a game in which a week is replayed continuously, but the tough deadline changed their plans, and the famous three day cycle of Majora's Mask was born.
Source: Zelda Informer