Kela felt something wrong with his elbow when he last pitched Tuesday against Houston.
General manager Jon Daniels said the options for Kela include rest or surgery, with surgery being the most likely outcome. But an MRI showed no issues with any ligaments.
Kela appeared in seven of the Rangers' first 14 games. As a rookie last season, he was 7-5 with a 2.39 ERA in 68 appearances.