The left-hander allowed solo home runs to Cesar Hernandez and Harold Ramirez, then left after Eddie Rosario's two-out single. Manager Brandon Hyde then came to the mound along with head athletic trainer Brian Ebel, and Means exited the game.
Means said he felt it when he was warming up, and later when he was extending while releasing his pitches in the first inning.
"It's not major,'' Means said. "It's nothing serious. It's more annoying than anything. I'm going to try and flush it out right now and try to attack some weak areas that are there."
Means had gone at least five innings in all but one of 11 starts this season. His 2.05 ERA at the start of the day (which rose to 2.28) ranked second in the AL, while his .173 opponents' batting average was third in the league.
Information from The Associated Press was used in this report.