Turner, 22, hurt himself during batting practice on Tuesday. He allowed five runs in six innings in his first start after going 3-8 with a 3.74 ERA (102 ERA+) in 20 starts and 118 innings in 2013. Miami acquired him from the Tigers in the Anibal Sanchez trade.
Right-hander Arquimedes Caminero was called up Triple-A to fill the roster spot. The 26-year-old had a 2.77 ERA (142 ERA+) with 12 strikeouts in 13 innings last season, his MLB debut.