The complaint centred around Byron Castillo, a defender who played in eight of Ecuador's qualifiers for the World Cup.
The Chilean football federation (FFCH) said there was evidence that Castillo, who plays for Leon in Mexico, was born in Colombia in July 1995 and not in Playas, Ecuador in November 1998.
The FFCH alleged "use of a falsified birth certificate, false declaration of age and false nationality".
Following a hearing on Thursday, FIFA's Appeal Committee confirmed an earlier ruling by the Disciplinary Committee.
"On the basis of the documents presented, the player was to be considered as holding permanent Ecuadorian nationality," FIFA said.
The FFCH reacted with fury, saying that Castillo had refused to appear at the hearing.
"This is a dark day for football and for the credibility of the system. The footballing world heard a player who helped Ecuador qualify for the FIFA World Cup admit he was born in Colombia and that he gained an Ecuadorian passport using false information. No wonder he refused to participate in the FIFA hearing," said Jorge Yunge, the FFCH general secretary.
With just over nine weeks until the opening game on November 20, Chile or Peru can still appeal to the Court of Arbitration for Sport.
"I have never seen in my entire life as a lawyer an injustice like this one," said Eduardo Carlezzo, the lawyer for the FFCH. "Sad day for football and for fair play.
The message is clear: cheating is allowed. We will appeal to CAS."
Ecuador finished fourth in South American World Cup qualifying to secure the last automatic regional berth.