The star Atletico Madrid striker has been plagued by recent hamstring problems, and was substituted after just eight minutes in his side’s UEFA Champions League final loss to Real Madrid on Saturday.
Dr Pedro Guillen of the Madrid general hospital CEMTRO confirmed the 25-year-old had come in for tests on Monday and revealed the extent of the forward’s injury.
"Diego Costa is still injured, he has a micro-tear in a hamstring," said Guillen. "He needs at least two weeks of rest."
La Furia Roja coach Del Bosque then emphasised the importance of every game at the World Cup finals, saying that he cannot risk bringing unfit players along with him to Brazil.
"We would like it if, on the second [of June] everyone is ready to train," said the Spanish manager. "We cannot bring players who are lacking fitness.
“The World Cup begins on the first day and we want all the players to be in good condition, so that they can play the game against Holland on June 13."
Del Bosque announced a 19-man squad to face Bolivia in a friendly on Friday which excluded striking duo Alvaro Negredo and Fernando Llorente, yet included inconsistent Chelsea forward Fernando Torres.
"We thought about Fernando,” said Del Bosque. “Apart from his numbers [goals this season], we have seen him feeling good.
“He has always done well for us. [But] Negredo and Llorente are not eliminated from the list of 23."
Torres, who has not featured for Spain in almost a year, said he was glad to be back and was overjoyed to be included in the squad for Friday’s friendly.
“It's very nice to be back with the national team,” said the Blues striker. “I've gone a year without being with La Roja, since the Confederations Cup.
"I knew that anything could happen. Yesterday, I was only hoping to hear my name. I knew that I could've been here or not, but now I have a better chance of being in Brazil.”
Spain are in Group B in this year’s Mundial alongside Chile, Australia and the Netherlands.