Kagawa featured in United's two games in Japan this past week.
"We've given Shinji more holiday because of his football with Japan in the summer," Moyes told reporters. "We try and give all players four weeks, if possible, and Shinji hasn't quite had that time. So we'll give him another week's rest. I think Shinji's going to do some training with the club, so he can have some more time at home in Japan. He'll do some training here."