The striker was not selected for Manchester United's trip to Liverpool in the Premier League and Moyes explained he expected Rooney to be out for "a few weeks."
Rooney was named by Roy Hodgson in England's squad for their crucial qualifying matches against Moldova and Ukraine, however he will not be available for the national side.
Moyes explained that the 27-year-old had sustained the injury during training in the build-up to their clash at Anfield.
"Wayne Rooney has got a cut down his forehead, it was completely accidental," Moyes told Sky Sports. "It will keep him out for a few weeks.
"I would think he's got no chance of playing for England."
Rooney's first start of the new season was for England against Scotland, and he also started in United's last fixture against Chelsea, a 0-0 draw, despite reports linking him with a move away from Old Trafford to Stamford Bridge.
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