Yamal suffered the injury playing for Barcelona on April 22. He was ruled out for the rest of the La Liga season, but de la Fuente said he had no doubt the 18-year-old would be available when the coach included him on Spain's 26-man roster on May 25.
It was thought that Yamal might miss part or all of the group stage, but de la Fuente said on Wednesday he expects him to be fit to face Cape Verde in Atlanta. However, he will not play in Thursday's friendly against Iraq, along with fellow injured Spain players Nico Williams and Víctor Munoz.
"If nothing changes, he could be ready to play on June 15," de la Fuente said at a press conference in Las Rozas, Madrid.
"It doesn't mean that for sure he will play, we'll see. Maybe a few minutes, maybe just practice so he can improve his condition for the second match. We will have to evaluate."
Spain play Peru in Mexico on Monday before travelling to their World Cup training camp in Chattanooga, Tennessee.
After their opener against Cape Verde, Spain play Saudi Arabia on June 21 in Atlanta and Uruguay on June 26 in Guadalajara.
Yamal finished second in the 2025 Ballon d'Or voting for the best player in the world. He also helped Spain win the Euro 2024 title after turning 17 during the tournament.
He has six goals in 25 appearances for the Spanish national team.