A nasty ankle injury sustained in his country's opening match means he will return to United's training complex for treatment.
Speaking after the 4-1 win over New England Revolution, Fergie said: "Antonio has gone straight back to Manchester.
"He got an injury playing in the first game for Ecuador so he is back in Manchester.
"It is nothing serious but he wasn't going to be taking part in the rest of Copa America, so there is no point in him coming out here if he is injured.
"We have the facilities back at Carrington. That is the best place for him."