Catcher Yasmani Grandal, right-hander Lucas Giolito and left-hander Gio Gonzalez will work into form slowly early in camp as they deal with minor ailments.
"We expect all of these guys to be fine by Opening Day," Hahn said. "We are dealing with three minor issues right now that are slowing down a few guys."
An MRI confirmed that Grandal has a mild calf strain. Because of that ailment, he'll miss the first week of Cactus League play, Hahn said. The White Sox's opener at spring training is Feb. 22, meaning Grandal could see game action around the start of March.
"If this was the regular season, we would quite frankly push through," Hahn said of Grandal's issue.
Giolito experienced soreness in his rib cage recently and was found to have a mild chest strain in that area. Giolito is the ace of the staff after an All-Star season in 2019.
"He was throwing today but will be behind our other pitchers," Hahn said Wednesday. "He will also miss the first week of games."
Gonzalez noticed discomfort in his throwing shoulder a few weeks ago, so the White Sox shut him down from throwing and gave him treatment. Gonzalez feels "great," but the White Sox will be cautious with him.
"He will be a little behind as well," Hahn said. "He likely will not participate in the first week of spring games. We expect him to be ready to go when the bell rings at the end of March."