Johnson, 29, pitched well at Triple-A, posting a 2.86 ERA with 20 strikeouts and eight walks in 22 innings.
"He was throwing very well," manager Ron Gardenhire said. "He was the recommended guy. He also threw the ball well for us in Spring Training."
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.