Greene wasn't able to report to spring training because of a "recurrence of issues he's dealt with in the past," general manager Jon Daniels said agent Mike Milchin told him Monday.
"We signed Khalil to help the club," Daniels said Thursday. "He's not able to do that right now. This was the cleanest way to address the contract situation. It doesn't preclude us from staying in touch, which we'll do. The priority is getting him well, and if he's ready to join us later on we'll address that then."
Greene, 30, was signed by the Rangers in January for a one-year, $750,000 contract.
He dealt with social anxiety issues last season, spending two separate stints on the disabled list and missing 46 games with the St. Louis Cardinals. He hit .200 with six home runs and 24 RBIs in 77 games.