The move creates a roster spot for left-hander Matt Harrison to be activated from the disabled list Saturday.
Feliz was 1-2 with six saves and a 4.58 ERA in 18 appearances this season. He went on the DL in late May with an abscess on his right side.
He and the Rangers had struck a one-year deal worth $4.125 million in January.
ESPN.com's Calvin Watkins and The Associated Press contributed to this report.