The Costa Rica full-back broke his tibia and fibula playing for Everton in their FA Cup fourth-round victory at Stevenage in January.
Oviedo was immediately ruled out for the rest of the season but was making good progress to be fit in time for the World Cup in Brazil.
However, Costa Rica team doctor Alejandro Ramirezhas confirmed he will need more recovery time and will not be lining up against England in the final Group D game on June 24.
"Today he was told to do some physical activity on a hard surface and showed some pains during the activity," said Ramirezhas.
"It means the player will be in no physical nor medical shape to play the World Cup."
Costa Rica coach Jorge Luis Pinto added: "Bryan was an important player, useful in our formation, where he fitted in very well.
"The squad are hurt as Bryan had fitted in very well, I hope his recovery happens in the best possible way for him."
Oviedo himself also confirmed on Twitter that he will miss the World Cup, tweeting: "I just got the news. I gave my best, but I can not be at the World Cup. I know my team are going to do a great job. Thanks for the support!"