The Manchester United man is in Brazil as back-up to Spain's number one Iker Casillas, together with Pepe Reina.
However, De Gea's presence at the tournament could now be in jeopardy.
An official statement from the the Spanish national team, released on their website, read: "David De Gea will not participate in the training of the Spanish team in Curitiba, due to muscual injuries.
The medical services of the Spanish national team will see the day-to-day evaluation of the goalkeeper in order to determine David de Gea's physical condition.
After running tests on David de Gea, it has been decided that he will not take part in the afternoon training session due to muscular discomfort in the gluteal region.
Spain were thumped 5-1 by the Netherlands in their opening Group B fixture and face Chile on Wednesday.
De Gea, who has only one international cap, was named in Spain's squad after Barcelona's Victor Valdes was ruled out through injury.
