Eloy Jimenez is expected to be sidelined for five to six months after rupturing his left pectoral tendon trying to make a play in the outfield during an exhibition game this week.
"Obviously a difficult loss for us, important part of our offense, and one that is a bit of a shock to the system," Rick Hahn said.
"At the same time, if there was one area of this team that perhaps could withstand a significant blow, it would arguably be on the offensive side of things."
Jimenez, 24, hit .296 with 14 homers and 41 RBIs in 55 games during the pandemic-shortened season.
As the Chicago White Sox search for replacements in left field, Leury Garcia, Adam Engel, Nick Williams and Billy Hamilton are candidates.