The winger picked up an ankle injury in Ecuador's first game against Paraguay, although was expected to return for El Tricolor's third group-stage game.
The knock has proved more troublesome, however, and Sir Alex revealed Valencia has left the Ecuador's Argentina base to continue treatment at United's training complex.
“Antonio's gone back to Manchester,” he said. “He got an injury playing in the first game for Ecuador so he's back in Manchester.
"It's nothing serious but he wasn't going to be taking part in the rest of the Copa America, so there's no point in him coming out here [to the USA to join us on the pre-season tour] if he's injured. We've got the facilities back at Carrington – that's the best place for him.”