"He came in today and was complaining of a sore shoulder, so we're going to get him checked out and shut down," Miami manager Mike Redmond said.
In 2013, Alvarez opened the season on the disabled list with shoulder inflammation. He didn't return until July 4. The Marlins are hopeful this setback isn't as serious.
"I don't know if it is in the same spot or the same type of pain he had last year," Redmond said. "We're going to get him checked out and make sure that we get him healthy. Hopefully we caught it early enough so it's not a huge deal."
Alvarez (8-5) is coming off a win against the Nationals on Tuesday, tossing seven shutout innings. But in the second inning, with the bases loaded and no outs, the right-hander appeared to show some sort of discomfort.
It was troublesome enough that Redmond and assistant trainer Mike Kozak went to the mound, but Alvarez stayed in the game, got out of the jam, and made it through seven innings.
Redmond said that Alvarez's shoulder bothered him late Thursday night, and on Friday, the 24-year-old informed pitching coach Chuck Hernandez that his arm was hurting.
"It kind of tightened up on him last night when he was sleeping," the manager said. "He came in and told Chuck and the trainers. We're going to get him checked out."
An MRI exam is expected for Alvarez, whose DL stint is retroactive to Wednesday.
In 22 starts, Alvarez is 8-5 with a 2.48 ERA and three shutouts in 137 2/3 innings.
Miami is looking to make a playoff push, which is a reason it acquired Cosart from Houston on Thursday. When that deal was made, Turner was set to move to the bullpen. But he will remain in the rotation for now. The right-hander is 4-4 with a 5.68 ERA in 11 starts. He's also thrown 15 2/3 innings of relief.
Reliever Dan Jennings, who was optioned to Triple-A after Thursday night's loss, was recalled to take Alvarez's spot on the active roster.