Kipnis suffered the injury while grounding into a double play during the fourth inning of Tuesday's game against the Los Angeles Angels. The move is retroactive to April 30.
The slumping Indians, who went 0-6 on a West Coast trip against the San Francisco Giants and Angels, called up Jose Ramirez, who was hitting .319 with four homers and 17 RBIs at Triple-A Columbus, to fill the roster spot.
Kipnis, who signed a six-year, $52.5 million contract prior to the season, is batting .234 with three home runs and 12 RBIs in 26 games.
The first-time All-Star had 17 homers and 84 RBIs in 2013 -- both career highs -- becoming the first Indians second baseman to lead the team in RBIs since Joe Gordon in 1948.
The Associated Press contributed to this report.