Gardenhire said Hardy's strained left wrist remains too painful for him to play.
"[Hardy's] still sore," Gardenhire said. "We are not ready to put him on the field. We just have to give him another day or two. Hopefully, we can get to the off-day and see where we are at against the White Sox."
Minnesota opens a series with Chicago Tuesday.
Hardy injured his wrist when he slid into third base after his ninth-inning triple in Minnesota's victory over Detroit on Tuesday.
Minnesota reliever Jose Mijares pitched one inning for Triple-A Rochester on Friday, giving up four hits and three runs in the Red Wings' 16-3 loss to Louisville. Despite his performance, Gardenhire remained optimistic Mijares could join the Twins' relief corps soon.
"[Mijares] didn't throw great," Gardenhire said. "He gave up a home run, but the ball was coming out of his hand, they said, great. We will get him back out there Sunday, and see how he is."
Gardenhire said there was a chance Mijares could join the Twins as early as Tuesday against Chicago.
Mijares suffered a strained elbow when Minnesota placed him on the 15-day disabled list on April 17.