Costa Rica face England, Italy and Uruguay in Group D in Brazil.
"After hearing the doctor's opinion and talking with the player we have to face up to the reality - Alvaro will not be at the World Cup," said Pinto.
"We hope he recovers enough to at least be able to travel to Brazil with us. I feel really sorry for him."
Pinto said he would not bring in another player given he has yet to cut his provisional squad down to the final 23.
The 32-year-old Saborio, who plays for Real Salt Lake in Major League Soccer, has scored 32 goals in 93 games for his country.
His club released a statement that he would be out of action for "three to four months" and was returning to Salt Lake to be further evaluated by the club's medical team.
Costa Rica are already without versatile left-sided player Bryan Oviedo who broke his leg playing for his English club Everton in January.
(Reporting by Simon Evans in Miami; Editing by Ken Ferris/Greg Stutchbury)
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