Meche pitched the first three innings of a 9-5 victory over the Chicago White Sox and gave up three runs on four hits before ending his outing.
"There's no pain going on so I'm not worried about it," Meche said.
But there was enough stiffness in his throwing shoulder that he was concerned that another inning or two might cause more problems.
"I think I'm in a position now to where I didn't want to keep pushing it with the season coming up," Meche said.
"I don't have a feel for my breaking ball too much. I keep saying that every time I pitch and I keep thinking it's going to turn the corner but I just kind of have some shoulder stiffness. It's nothing serious."
Meche is scheduled to have two more Cactus League starts before pitching the season's second game on April 7 at Kansas City.
He had experienced some stiffness earlier and underwent some tests.
"They checked me out, the shoulder's strong but the tightness is there. I don't feel real strong when I'm pitching," he said.
"So I just kept working through it and after the third inning, it was like well, I've had enough. I didn't want to keep going, I felt like I was getting stiffer in a way, I'm not throwing any good pitches. Just take it easy on this one and then see what happens my next one."
Last season Meche did not pitch after Aug. 29 because of fatigue in his right shoulder. That, however, was believed to have been accentuated by back problems which he's not experienced this year.
"Last year I did push through things and I know where that got me so I want to make sure I feel 100 percent when the season starts so it's a matter of me being smart right now," he said.
So far this spring Meche has pitched four games and has a 2-2 record with a 6.55 ERA. He's pitched 11 innings.
On Monday, he left the game after throwing 56 pitches (31 strikes).
"Right now I'm going to make sure I do the right things so it'll go away," Meche said.
Dick Kaegel is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.