Rooney incurred a cut in training and was forced to sit out their Premier League clash with North West rivals Liverpool at Anfield on Sunday.
That leaves his participation in Friday's game at Wembley and Tuesday's match in Kiev in serious doubt, with Moyes admitting he does not expect him to feature.
"He got a cut down the middle of his forehead, completely accidental, but it was quite a bad cut," Moyes told Sky Sports.
"It will probably keep him out for a few weeks."
As for whether Rooney would be able to turn out for England, Moyes added: "I would think no chance."
Moyes also confirmed he had planned to start with Rooney against Liverpool.
"He was in our team to start and he would have started had he been fit," added Moyes.
If Rooney is forced to withdraw from Roy Hodgson's squad, the England boss would be left with just Jermain Defoe, Rickie Lambert, Daniel Sturridge and Danny Welbeck as out-and-out strikers.