Kennedy was placed on the 60-day injured list Saturday due to a rotator cuff strain, Kennedi Landry of MLB.com reports.
The Rangers selected Kennedy's contract from Triple-A Round Rock on Tuesday.
Kennedy re-signed with the Rangers on a minor-league contract June 13.
Kennedy elected free agency Sunday after refusing an outright assignment to Triple-A Round Rock.
Kennedy was designated for assignment by the Rangers on Thursday.
Kennedy allowed five runs (four earned) on two hits and two walks over a third of an inning in Saturday's 8-2 loss to Houston.
Kennedy threw a perfect eighth inning in Friday's 2-0 loss to the Cubs.
The Rangers selected Kennedy's contract Wednesday, Kennedi Landry of MLB.com reports.
Kennedy allowed one walk over a scoreless sixth inning in Saturday's spring game against the Angels.
Kennedy signed a deal with the Rangers on Thursday, he announced on his personal Instagram account.