The team did not give a reason for the IL move.
Mazara, 25, hit .268 with 19 home runs, 66 RBIs and a .786 OPS for the Texas Rangers last season before being traded to the White Sox at the winter meetings in December.
"He's a young man who is going to be extremely helpful to us," manager Rick Renteria said Wednesday. "Sooner we get him back, the better."
The White Sox open their season at home against the Minnesota Twins on Friday.
The Associated Press contributed to this report.