The Japan international has not played since sustaining the injury in the UEFA Champions League victory over Braga at Old Trafford on 23rd October.
The 23-year-old was initially expected to be back in action within four or five weeks.
However, United manager Sir Alex Ferguson said: "His progress has been quite slow actually.
"He hasn't started any outside work and, looking now, he may be another four weeks away.
"Overall, he will probably be looking at six to seven weeks since the injury. The first job now is to get him back."
Kagawa had started the season strongly with United following his £12m move from Borussia Dortmund in the summer and had scored two goals in eight appearances before being stopped in his tracks by the injury.