Kagawa was expected to be sidelined for up to a month after picking up the problem in the October 23 victory over Braga in the Champions League but Ferguson said the 23-year-old's recovery had been slower than expected.
"He's not started any outside work and we're looking at another four weeks away, which is disappointing," he told reporters ahead of Tuesday's Group H clash with Galatasaray.
"Originally we thought three or four weeks - now it looks like seven or eight weeks," Ferguson added on United's website.
United, already assured of qualifying for the Champions League knockout stages, had earlier announced that they would rest a number of senior players for the game in Istanbul.
Wayne Rooney, Rio Ferdinand, Ryan Giggs, Paul Scholes, David de Gea and Robin van Persie have all stayed in Manchester, United said on their website.
JONES RETURNS
However, United's England defender Phil Jones is expected to start against Galatasaray after recovering from a knee operation and a back injury which have kept him out so far this season.
"It's a big day for Phil Jones," said Ferguson. "He's been out all season but he's done enough training now to make sure his fitness is OK. I'm looking forward to bringing him back."
"Phil's had different types of injuries [at United]. He had concussion, he had a rib injury... but he's young so he's still to develop physically in terms of his body. He's only 20 years of age so there's plenty of time for him."
United's squad includes seven players yet to feature in the competition but Ferguson is sure they won't let United down.
"We don't consider the young players a gamble," he added. "What we do consider is our reputation and we have to be fair to the other teams in the group."
United, with a maximum 12 points from four games, have reached the last 16 with two games to spare. Galatasaray and CFR Cluj have four points with Braga bottom of the group on three.
