Enzo is the son of former Los Blancos boss, Zinedine Zidane, who left the club after they won a third successive Champions League trophy in May.
The 23-year-old joined Real Madrid’s youth academy in 2004 at the age of 9 and trained with the first team as early as 2011.
He featured in the Copa del Rey for Real, but has yet to make his debut for the Spanish giants in the La Liga.
A statement on Majadahonda’s website reads: “After several weeks of contact, and despite having several offers elsewhere in Spain and also abroad, Enzo Zidane has committed his belief to the project that is being built at CF Rayo Majadahonda for the club’s first season in professional football.
“It is an indication of what the club is aiming to achieve for the future and the sporting plans that have been developed for several years.
“All parties have made a great effort to reach an agreement of a loan for one year, although the intervention of the first-team coach Antonio Iriondo has been decisive in convincing the player of the importance he can have in the team and the professional growth that he can achieve this season in the league.”