The utility infielder is struggling with social anxiety disorder, a condition which landed him on the disabled list twice last year with the St. Louis Cardinals.
"The Rangers fully support Khalil's decision to address this private matter," Rangers general manager Jon Daniels told MLB.com. "Per club policy, we will not comment on his medical situation. We have agreed to leave the door open for a continued relationship, if both Khalil and the team desire that in the future."
Texas singed Greene to a one-year contract this offseason. Green played 77 games with the Cardinals last season, hitting .200 with six homers and 24 RBI in 170 at-bats. He played with the San Diego Padres from 2003-08.