The Manchester United keeper is suffering from a gluteal muscle problem but it is unclear how long he will be sidelined for.
"After undergoing tests it was decided that David de Gea would not take part in the team's afternoon training session owing to muscle discomfort in the gluteal region,” read a statement from the Spanish football federation (RFEF).
"The Spanish national team's medical services will evaluate day by day the goalkeeper's recovery to determine his reincorporation into the group."
Spain’s first choice goalkeeper Iker Casillas came in for some criticism for his performance in their shock 5-1 defeat to the Netherlands on Friday and De Gea could be in line to replace him for their next Group B game against Chile on Wednesday.
He will be closely monitored before that game in Rio de Janeiro, with former Liverpool keeper Pepe Reina also in contention to feature if national head coach Vicente del Bosque opts to make changes.
Spain’s final group match is against Australia in Curitiba on Monday.