The 23-year-old complained of a pain in his lower back and could be a doubt for the Red Devils' upcoming matches against Wigan and Galatasaray
The 23-year-old played in Japan's 1-0 win over UAE last week but was named on the bench by his national side's boss Alberto Zaccheroni for the match against Iraq.
Kagawa played the first half in the match against UAE, but was substituted at halftime after Zaccheroni was reportedly frustrated with one of his star players' displays.
A Japan Football Association official told Japan's Daily Sports: "He felt uncomfortable in his lower back in practice yesterday, and we decided to wait a night and see how it looked, but he's not at 100% so we're leaving him off. He didn't go to the hospital."
Manchester United hosts Wigan on the Premier League on Saturday before kicking off its Champions League campaign next Wednesday with another home match against Turkish side Galatasaray.
Kagawa has impressed since completing his move to the club over the summer from Borussia Dortmund and Red Devils boss Sir Alex Ferguson will be hoping he can recover from the injury.