The move is retroactive to April 4.
Turner was scratched from his scheduled start Wednesday against the Washington Nationals and was replaced by left-hander Brad Hand. Turner still had tightness in the shoulder on Wednesday and he was sent home to Miami for an MRI.
Turner's roster spot was taken by reliever Arquimedes Caminero, who was recalled from Triple-A New Orleans.
"He was still a little bit stiff, so we sent him back to Miami to get an MRI," manager Mike Redmond said. "We hope to know more tomorrow. Obviously, he's going to go on the DL. Caminero was here, in anticipation of this happening."
In one appearance this season on April 3 against the Colorado Rockies, Turner pitched six innings, giving up eight hits, five earned runs and walked three, earning a no-decision.SI.COM STAFF: Power Rankings: Detroit Tigers nab top spot in first week of voting