"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."
Asked about Rooney playing for England, Moyes added: "I would think no chance."
Moyes had intended to start Rooney at Anfield too.
"He was in our team to start and he would have started had he been fit," the Scot said.
If Moyes is correct and Rooney does withdraw from England duty, national team boss Roy Hodgson is left with Jermain Defoe, Rickie Lambert, Daniel Sturridge and Danny Welbeck as out-and-out strikers.
England face Moldova at Wembley on Friday and then travel to Ukraine for a vital clash a week on Tuesday.
Rooney's injury comes just as he seemed to be embarking on a period of stability after a testing summer.
Former United boss Sir Alex Ferguson retired in May and said before leaving that the striker had asked to leave the club and, although Rooney never confirmed it, he was heavily linked with a move away.
Chelsea made two bids to try to lure him to London and that looked even more likely when Rooney was reported to be "angry and confused" about his standing at Old Trafford following comments made by Moyes on the club's pre-season tour of the Far East and Australia.
A starting and starring role in last Monday's draw with Chelsea appeared to have paved the way for a United future, though, and Blues boss Jose Mourinho then conceded defeat in his bid to sign the 27-year-old.