Pedri had to be substituted in the early stages of Friday's quarter-final with Germany after a heavy challenge from Toni Kroos.
The Barcelona midfielder was in tears when he left the field, and the Spanish Football Federation have now confirmed that Pedri has suffered a medial collateral ligament sprain in his left knee.
As a result, the 21-year-old will not play again at Euro 2024.
Spain suffered two more blows during the match, with Le Normand's 29th-minute yellow card seeing him ruled out of the France game through suspension.
Le Normand, Carvajal will both be banned for Spain
Carvajal was booked in the 100th minute, which alone would have seen him suspended for the semi-final.
However, the Real Madrid defender was then sent off in the final stages for preventing a Germany break on the Spain goal.
As a result, Spain will be missing two of their defensive starters against Didier Deschamps's side, which could open the door for Nacho and Jesus Navas to come into the starting XI.
France booked their spot in the final four of the competition courtesy of a penalty-shootout success over Portugal, with the two teams playing out a goalless draw.
Spain's game with Germany also looked to be heading for penalties, with Florian Wirtz cancelling out an opener from Dani Olmo, but Mikel Merino scored the winner for La Roja in the 119th minute.
De la Fuente calls it "a historic night"
"This is the moment to appreciate what we've achieved and enjoy this moment. Physically we'll see how we can improve in the next few days. I'm sure that all of my players are ready [for the semi-final]. They're playing at a very high level," Spain boss Luis de la Fuente told reporters.
"This is a historic night. I'm proud to be able to represent our country. How far we get, we will see, but we're absolutely convinced that we can get very far with this team.
"My players are insatiable. I'm proud to coach players like this. I've known many of them for many years. They're used to competing at the highest level and they have an opportunity to win [the tournament]. This team are always going to compete. There's always room for improvement, of course, but we can't question their pride, quality and commitment.
"Our euphoria is totally under control. We're so happy, but we know that tomorrow is already another day. We can't control what happens on the outside, but we're thrilled that the country is supporting us."
Should Spain overcome France, they would face either England, Switzerland, Turkey or Netherlands in the final of the European Championship.