Manager Don Mattingly said Cooper underwent an MRI that revealed a mild left calf strain, Andre Fernandez of The Athletic reports.
Cooper suffered the injury over the weekend and was sent to the IL as a result. The 28-year-old said he isn't expected to resume baseball activities for a few weeks, suggesting his stay on the shelf could last more than a month. Peter O'Brien, who has started in right field each of the past two games, looks poised to fill in for Cooper for the time being.