Cole suffered the injury during a training session last month. Pirates trainer Todd Tomczyk told reporters Friday that the injury has limited Cole in his work at spring training.
"It's just a modified throwing program at this point," Cole told reporters. "I'm not too far behind everybody else, but I feel good."
Cole will not throw any bullpen sessions or pitch from an elevated mound until the Pirates determine that he is recovered from the injury.
Cole, 25, went 19-8 with a 2.60 ERA and was a first-time All-Star last season.