This is the first time in Price's career that he has been placed on the DL, according to MLB.com. He was removed early from his start on Wednesday after suffering the injury.
Prince, 27, won the American League Cy Young award in 2012 with a spectacular campaign but has struggled to begin 2013. This year he has made nine starts but has a 5.24 ERA and 1.436 WHIP.
Torres has been very good in seven starts for Triple-A Durham, posting a 2.39 ERA. He is a strikeout pitcher, with double-digit K/9s in 2012 and in 2013 so far. Control issues have come along with that, however, though it appears as though he has improved in that regard with a 3.3 BB/9 this season. Like Price, Torres is a lefty.
Torres made four relief appearances for the Rays in 2011, allowing three runs over eight innings.