Johnson, 29, was pitching well at Rochester, posting a 2.86 ERA with 20 strikeouts and eight walks in 22 innings.
"He was throwing very well," Twins manager Ron Gardenhire said. "He was the recommended guy. He also threw the ball well for us Spring Training. So we'll see how it goes."
Johnson said the key to his success at Triple-A was establishing his fastball command to set up his cutter, curveball and changeup.
"I was able to locate my fastball pretty well and change speeds when I needed to," Johnson said. "Just miss the barrel."
Johnson, who was acquired in a trade with the Pirates in exchange for reliever Duke Welker in November, has limited Major League experience, as he made four appearances with the Pirates last season, including one start, posting a 6.10 ERA. He was hit hard in his one start, as he lasted just two innings against the Cardinals on Sept. 1.
Johnson said that nerves got the best of him in his first career start, but he doesn't expect that to be an issue Thursday.
"It's a different clubhouse and a different group of guys, but it's still the same game," Johnson said. "I got the jitters out of the way. So hopefully I can just go out there and pitch like I know I can."