The 18-year-old will spend one season in Italy under the current agreement, according to a brief announcement on Real's website.
Mastantuono signed at the Bernabeu last summer after catching the eye in his homeland with River Plate and becoming, aged 17 years and nine months, the youngest player to represent the Argentina national team in an official match.
He moved to Spain on a six-year deal after Real shelled out just over 63 million euros ($72 million) to secure his services.
The teenager made 35 appearances across all competitions last season for Los Blancos, scoring three goals, but failed to nail down a starting spot as he missed out on Argentina's World Cup squad.