The Deportivo Saprissa wing-back, 29, started in their 1-1 friendly draw with the Republic of Ireland on Friday, however, he felt a 'sharp pain' during training on Tuesday.
Team physician Vladimir Badilla confirmed Mora had suffered a stress fracture, but it was unclear whether the player's Achilles' tendon was the affected area.
Mora will be replaced in Jorge Luis Pinto's 23-man squad by Herediano defender Dave Myrie.
Costa Rica are drawn in Group D in Brazil, where they are up against England, Italy and Uruguay.
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