Kelley underwent an MRI Monday after he felt discomfort in his pitching arm as he was getting prepared to enter Sunday's game in Houston.
The results of the MRI were positive as the club says it showed that he only had muscle soreness in his biceps and "no acute injury." Kelley has been placed on the 10-day IL.
The 35-year-old is 5-2 and has converted 11 saves to go along with a 3.00 ERA. Kelley was one of several players contending teams would have an interest acquiring at next week's trade deadline. It's unknown how his injury will impact his market.
Texas called up reliever Rafael Montero to replace Kelley on the active roster. They also announced that they had designated minor league outfielder Carlos Tocci for assignment.