The teenager will miss the start of the new campaign and joins a number of his new team-mates in having picked up a knock during pre-season.
Real Madrid forward Rodrygo is set for up to three weeks on the sidelines after it was confirmed he has suffered a hamstring injury.
The 18-year-old completed his protracted move to Santiago Bernabeu from Santos this summer, and it was hoped - at least by supporters - that he would be able to make an impact in the first team this season.
Rodrygo has featured throughout pre-season for Zinedine Zidane's side, but will now miss the start of the new La Liga campaign as he nurses his way back to full fitness.
"Following the tests carried out by the Real Madrid medical department on our player Rodrygo Goes, he has been diagnosed with an injury on his right rectus femoris [hamstring]," Madrid's statement read.
"His recovery will continue to be assessed."
Rodrygo's move to Los Blancos was agreed during the summer of 2018, with Madrid paying Santos €45 million to acquire the teenager, though a decision was made that he would remain in Br azil to continue his development.
During his time with Santos he contributed 10 goals and five assists in 49 appearances, and was unveiled to the Bernabeu crowd ahead of this summer's pre-season programme.
Having followed a similar path to that of Vinicius Junior, who left Flamengo for Madrid during the summer of 2018, there is a belief that Rodrygo could follow his compatriot into the Madrid matchday squad in the months to come.
However, it is widely understood that he will begin the campaign playing for Real Madrid Castilla in the third tier of Spanish football and work under new coach and Madrid legend, Raul.
Rodrygo is not the only new arrival at the 13-time European champions to suffer an injury during pre-season, with Ferland Mendy and Luka Jovic also having missed matches due to thigh and ankle injuries respectively.
And while Jovic has since returned to action, Mendy is not expected to be back in contention until the end of August at the earliest.
Thibaut Courtois and Brahim Diaz also picked up injuries during Madrid's tour of the United States while Marco Asensio could miss the whole season after rupturing knee ligaments against Arsenal.
Madrid kick-off their new Liga season on Saturday as they travel to Vigo to take on Celta as Zidane looks to stabilise the club following a rollercoaster last 12 months.