The Pole suffered the injury in Tuesday's emphatic 3-0 win over Chelsea.
"This was the finding of a thorough examination by Bayern doctor Dr. Hans-Wilhelm Müller-Wohlfahrt upon his return from London on Wednesday today.
"After immobilization in a plaster cast for ten days, rehabilitation training will commence. He will be out in total for approximately four weeks."
Lewandowski will almost certainly miss the return leg at Allianz Arena on March 18.