However, there has been no structural damage found in Cole's right shoulder, General Manager Neal Huntington said.
Cole, a former UCLA pitcher, was the top overall pick in the 2011 amateur draft.
Texas Rangers first baseman Mitch Moreland will sit out about three months to have surgery on a left ankle that has been bothering him all season.
Moreland has tried injections and other remedies but hasn't been able to get rid of persistent pain in the ankle.
The 28-year-old Moreland had to take over at first when Prince Fielder was sidelined for the season to have neck surgery. Moreland is hitting .246 with two home runs and 23 runs batted in. He had a career-high 23 home runs last season.
Hunter, sidelined because of a left groin strain, is 1-1 with a 6.06 earned-run average and leads the team with 11 saves in 14 opportunities. He hasn't pitched for the Orioles since May 20.