The England man picked up an ankle injury when he was challenged by Pablo Zabaleta during the second half of United's 2-1 loss and Shinji Kagawa was brought on.
Young's injury is not as bad as first feared but this weekend's fixture is likely to come too soon for the 27-year-old.
United boss Sir Alex Ferguson said: "We've got six days until the Stoke game and, obviously, Ashley may be out.
"It may not be serious but I think he'll miss Sunday's game."
Ferguson is also worried about his lack of fit centre-backs, especially with a possible aerial bombardment to face at the Britannia Stadium.
Nemanja Vidic, Jonny Evans and Chris Smalling all missed Monday's match and Ferguson said: "We'll have to assess the centre-backs as the week goes on.
"We'll have to hope we can get them fit, particularly for the Stoke match, because we know what it's going to be like down there."