Allen was a major doubt having not played since September and Wales manager Rob Page has confirmed the midfielder has lost his battle to be fit to face the US.
His failure to recover from his hamstring injury in time leaves Page with a selection headache.
Allen, the 32-year-old former Liverpool midfielder who now plays for Swansea, is a key player for Wales.
“We said from the start we were going to give him every possible chance but he’s not going to make it if I’m being completely honest,” said Page.
“If he breaks down, he’s definitely out for the tournament. We’re not going to push him.”
After playing the United States on Monday, Wales face Iran four days later and then meet England in their final Group B game on November 29.
Wales will hope Allen will be fit to feature against Iran.