Kennedy's last appearance was in 30-pitch outing Friday night at home against Tampa Bay, when he got his 12th save of the season. It was the right-hander's first save opportunity in two weeks.
The Rangers brought right-hander Spencer Patton up for Triple-A Round Rock before their home game against San Francisco.
When Kennedy didn't pitch with the Rangers leading in the eighth inning Tuesday night, manager Chris Woodward said afterward that the closer wasn't available because of the hamstring issue that had been bothering him for a few days.
Kennedy has a 2.53 ERA in 21 relief appearances, going 12 of 13 in save opportunities. He is eligible to return June 16, because the IL move was retroactive to Sunday, and Woodward said that he anticipates the 36-year-old reliever being ready then.