The Pirates acquired the veteran slugger from the Baltimore Orioles at last month's trade deadline. He sustained the injury when he was hit on the wrist Aug. 3 by the Chicago Cubs' Carlos Marmol.
Lee was able to play two games after missing four contests following the injury, but a decision to shelve him was made following batting practice Friday in Milwaukee before a game with the Brewers.
Lee appeared in just five games for the Pirates, hitting a pair of homers in his first contest with the club but compiling just three hits after that. He is hitting .247 with 14 homers and 47 runs batted in 90 overall games this year.
The Pirates recalled infielder Josh Harrison from Class AAA Indianapolis to fill the roster spot.