Bailey was placed on the 60-day disabled list Wednesday with an elbow ligament strain.
Bailey had made two starts this season, posting a 5.56 ERA in 11.1 innings.
A nine-year veteran, Bailey has thrown two no-hitters in his career. He was 33-27 with a 3.61 ERA over the past three seasons.
Bailey, 28, is a former Reds first-round pick and top prospect. He signed a six-year, $105 million extension with Cincinnati in February 2014.
Rookie Michael Lorenzen took Bailey's place in the rotation and allowed three runs in five innings in his Major League debut Wednesday.
- Alex Putterman