Castillo suffered a torn ACL when he collided with Mexico midfielder Luis Montes during Ecuador's 3-1 friendly loss to El Tri on May 31. Montes fractured his tibia and fibula on the play.
Minda, 30, was included in Reinaldo Rueda's provisional 30-man squad for the tournament, but will now join up with his teammates to step in for 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.
Minda has made 46 appearances (43 starts) over three seasons with Chivas USA. He has started all eight of his matches this year.
Ecuador has been drawn in Group E for the World Cup, alongside France, Switzerland and Honduras.