The 21-year-old arrived at Bernabeu from Flamengo in 2020, but he is yet to make a first-team appearance for the Spanish giants.
Reinier spent the 2020-21 and 2021-22 campaigns on loan at Borussia Dortmund, but he found it difficult to make his mark, only managing one goal and one assist in 39 appearances.
The Brazilian spent last season on loan in La Liga with Girona, meanwhile, featuring on 18 occasions, finding the back of the net on two occasions.
The forward is not in Carlo Ancelotti's plans for the 2023-24 campaign, though, and he has now been allowed to make the move to Italian side Frosinone.
"Real Madrid CF and Frosinone Calcio have agreed on the loan of the player Reinier for this season, until June 30, 2024," read a statement on the Spanish club's official website.
There is not believed to be the option to make the move permanent, though, so the South American will head back to Bernabeu next summer.
Reinier has another three years left to run on his contract at Real Madrid, and a successful loan spell in Italy could help him kickstart his career with his parent club.
Real Madrid are currently preparing for their fourth La Liga match of the season at home to Getafe, which will take place on Saturday afternoon.
Vinicius Junior, Arda Guler, Thibaut Courtois, Ferland Mendy, Dani Ceballos and Eder Militao are currently unavailable for selection for the capital giants through injury.
However, despite Vinicius's thigh issue, Los Blancos will not be entering the market to bring in a replacement, leaving Ancelotti short of options in the final third of the field.
Joselu could be in line for a start on Saturday alongside Rodrygo in a front two, while 19-year-old forward Gonzalo Garcia has been called up for the contest with Getafe.
Real Madrid are currently top of the La Liga table on nine points, winning their opening three matches of the campaign against Athletic Bilbao, Almeria and Celta Vigo.