Rangers assistant general manager Thad Levine says Choo has stiffness in his triceps and will be given a day or two off.
Texas was playing the Chicago White Sox on Sunday.
Choo finished second in the NL last season with a .423 on-base percentage and scored 107 runs for Cincinnati. He signed a seven-year, $130 million contract in December with the Rangers.
Choo throws and bats left-handed.
Rangers shortstop Elvis Andrus was shut down with a sore arm Saturday.