The 29-year-old England international picked up the injury at the start of pre-season training.
“He is working hard on his rehabilitation to be available after the first international break,” United said in a statement.
United start their campaign at home against Fulham on Friday.
Meanwhile, French centre-back and new signing Leny Yoro, 18, will return to action in about three months following successful surgery on his foot injury, United had announced earlier in August.
--Reuters--