The Germany international suffered the problem early in Bayern's 2-0 victory in the first leg of their UEFA Champions League quarter-final tie with Juventus at the Allianz Arena.
Kroos was taken off after just 16 minutes, with Arjen Robben replacing him for the remainder of Tuesday night's clash.
Bayern's team doctor, Hans-Wilhelm Mueller Wohlfahrt, has revealed the 23-year-old will be out of action for "six to eight weeks".
The Bundesliga giants, who are bidding to become the first German side to win the league, Champions League and cup treble, are 20 points clear at the top of the table.
Coach Jupp Heynckes said of Kroos' injury: "It's very disappointing for him and for all of us.
"A lot will be decided in the next two months and his injury will take a long time."