Carrasco, who first felt the tightness during his warm up in the bullpen, was removed after the third when it started to get worse. He will be evaluated on Monday after the Indians return to Cleveland.
"He said he couldn't get it loose at all," manager Manny Acta said. "We kind of sensed some of that because the velocity wasn't where he was in the past, but he kept saying he was fine, just couldn't get it loose."
Carrasco said the tightness most affected him on the fastball, which caused his velocity to drop about five miles per hour on average from his last start. Finally, in the third inning, it became an issue.
After holding the Twins to just one hit over the first two frames, Carrasco got hit hard in the third, but some mistakes on the basepaths allowed him to escape with minimal damage.
Alexi Casilla and Denard Span led off the inning with a pair of singles and Jason Kubel added another with one out.
Following Kubel, first baseman Justin Morneau crushed a two-run double to center field that would have plated three runs, had Casilla not been thrown out at the plate by Shin-Soo Choo on Kubel's single.
Carrasco was replaced by right-hander Jeanmar Gomez, who was available after the Indians decided to push him back until Saturday after Friday's rainout and Monday's off-day forced them to alter their rotation.
"[Carrasco]'s going to be evaluated when he comes in, and then we'll schedule something," Acta said. "Now, with Carrasco [potentially] down, he can just slide right into Carrasco's spot. We'll have to see. We'll have to evaluate him tomorrow and see how he is."