Luhnow told reporters Thursday that the injury was found during testing this week. Pressly had complained of discomfort after pitching in Tuesday's win over the Detroit Tigers.
Pressly will be placed on the 10-day injured list but could return during the regular season, Luhnow said.
The 30-year-old Pressly has a 2.50 ERA with 65 strikeouts in 51 appearances this season. He had an MLB record streak of 40 straight scoreless appearances that was snapped by the Boston Red Sox in May.