Young hurt his shoulder in a collision with Tottenham Hotspur goalkeeper Hugo Lloris. The former Aston Villa player landed awkwardly as he leapt over Lloris and will certainly miss this weekend's FA Cup third-round meeting with Swansea City.
"Ashley has got an injury that is going to keep him out for a time," said Moyes. "It is a shoulder injury he received in the challenge by the goalkeeper. I am not sure how long it will be."
Meanwhile, Moyes offered no further update on the fitness of Robin van Persie, who has missed six games with a thigh injury. "We will let you know when he is ready," said the Scot.