Midfielder Castillo has lost his battle to be fit for the finals in Brazil after damaging his anterior cruciate ligament in his right knee during a 3-1 friendly defeat against Mexico on May 31.
Minda, who plays for Chivas in the MLS, was originally included in Reinaldo Rueda's provisional 30-man squad for the tournament, but will now join up with his team-mates to cover for the absence of Castillo.
"Despite the extraordinary skill and assistance of Segundo Castillo, (he) is unable to continue within the discipline and work of the group that makes up the Ecuadorian national team," read a statement on the Ecuadorian Football Federation's website.
Ecuador have been drawn in Group E for the finals, alongside France, Switzerland and Honduras.
They begin their campaign against the Swiss on Sunday, and will look to at least match their feats of their last appearance at the World Cup, when they reached the second round at Germany 2006 before losing 1-0 to England.
