Kroos went down in the 14th minute of the quarter-final first leg tie and the injury was worse than it first looked, the Bavarian club said.
Team doctor Hans-Wilhelm Mueller-Wohlfahrt said the Germany international had probably ruptured an adductor muscle in his right hip and could be out for six to eight weeks, effectively ending his season for his club.
"Obviously, this is a severe blow," said coach Jupp Heynckes. "A lot will be decided over the next two months."
Kroos has scored nine goals in all competitions this season.