The 18-year-old midfielder is expected to be out for around six weeks to two months, with the club hoping he can return in early to mid-September if his recovery goes as planned.
Real Madrid manager Jose Mourinho confirmed the injury is linked to a problem Pitarch picked up while on international duty with Spain Under-19s and said the club is trying to avoid surgery.
"I think his injury is serious. I don't know how long he will be out, but it is an injury that comes from the last time he went with the international team," Mourinho said.
"We are trying a conservative treatment. But, if the conservative treatment is not resulting, probably he will have a surgery procedure, but let's wait a little bit more."
The setback comes at a difficult time for Pitarch, who had returned to pre-season hoping to impress Mourinho and earn a place in the first-team squad.
Real Madrid's coaching staff had planned to assess the midfielder over the coming weeks before deciding whether he should remain with the club or spend the 2026-27 season on loan to gain valuable first-team experience.
With Pitarch now sidelined, the club may have to make that decision before he has the chance to prove himself in training or pre-season matches.
The injury could also affect interest from clubs considering a loan move, although regular playing time elsewhere is still seen as the best option for the promising midfielder's development once he has recovered.