Perkins wasn't available to pitch in Friday's 7-6 loss to the Angels in 10 innings, as he started to feel stiffness in his neck during his appearance on Thursday. Perkins gave up the go-ahead run in the ninth against the Angels in Thursday's 5-4 loss.
"He's going to be day to day and probably miss a few games here," Gardenhire said. "We're not going to even mess with him for a few days."
Right-handers Jared Burton and Casey Fien are expected to share time at closer in Perkins' absence. Burton was the closer in Friday's game with Perkins unavailable and surrendered the go-ahead run in the 10th inning.
Rhett Bollinger is a reporter for MLB.com. Read his blog, Bollinger Beat, and follow him on Twitter @RhettBollinger. This story was not subject to the approval of Major League Baseball or its clubs.