The complaint was only expected to keep the Japanese international out of action until later this month.
However, manager Sir Alex Ferguson has revealed that the midfielder's recovery is taking longer than originally anticipated.
"[Kagawa's] progress has been quite slow actually," Ferguson told reporters. "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 joined United during the summer from German champions Borussia Dortmund.