The striker missed the game at Anfield and is unlikely to join up with Roy Hodgson's England squad along with three casualties from Sunday's game on Merseyside.
Rooney's United teammate Phil Jones is another possible England absentee after being substituted during the first half of the contest with an ankle problem.
Meanwhile, Liverpool boss Brendan Rodgers believes Daniel Sturridge and Glen Johnson will also be unavailable for the brace of qualifiers. The former departed the ground on crutches.
England face Moldova at Wembley this Friday, while the Ukraine match takes place in Kiev the following Tuesday.
As for Rooney, his manager Moyes said: "He got a cut down the middle of his forehead, completely accidental, but it was quite a bad cut.
"It will probably keep him out for around three weeks."
With Rooney and Sturridge set to miss the vital Group H games, it leaves Hodgson with just Jermain Defoe, Rickie Lambert and Danny Welbeck as out-and-out strikers.