Nathan left after walking two batters and striking out one in the third inning of the Boston Red Sox 9-3 win.
"Supposedly, there wasn't a lot of concern, but we'll see," Gardenhire said. "It's coming off a surgery and it's the same spot and that's normal. ... I think he'll be fine."
Nathan returned to the Twins stadium, also in Fort Myers, where team doctors checked him, Gardenhire said.
"Just general soreness just like it always is when you throw," Gardenhire said. "He felt stiffness out there pitching and, as he told me, he just felt a little tight and we're not going to push that at all. Get him off the mound and we'll go from there."
Gardenhire added that Nathan had felt fine ever since reporting to spring training.
Nathan was second in the majors last season with 47 saves then had surgery in October to remove bone spurs and bone chips.
The Associated Press contributed to this story.