The Japan international suffered the problem in a 3-2 victory over Braga in the Champions League at Old Trafford back in October.
It was initially thought the 23-year-old would be out for four weeks, but the former Borussia Dortmund man has taken longer than expected to recover from the setback.
“Shinji’s progress has been quite slow actually,” said Ferguson. “He’s not started any outside work and we’re looking at another four weeks away, which is disappointing.
“Originally we thought three or four weeks – now it looks like seven or eight weeks.”
Kagawa has scored two Premier League goals in six appearances after completing a move to the Red Devils in June.