The move was made retroactive to Saturday.
Sosa suffered the injury before Sunday's game at San Diego when he suffered back spasms during a sneeze.
Losing Sosa is another blow for the Cubs, who are without star pitchers Mark Prior and Kerry Wood. Prior is on the 60-day DL with a sore right Achilles tendon and Wood is day-to-day with a strained right triceps that forced him to miss a start.
Despite the injuries, the Cubs entered Wednesday's action one game behind first-place Houston in the National League Central Division.
Sosa, 35, is hitting .291 with 10 homers and 24 RBI in 35 games. On Saturday, he slugged his 549th career homer, moving past Hall of Famer Mike Schmidt into ninth place on the all-time list.
Celebrity Families of 2014 [PHOTOS]