The right-hander apologized to his teammates and fans in a statement issued through the players union Wednesday while saying he will be "away from the team while I get the help I need to overcome these difficult personal issues."
Jeffress was arrested Friday. He was twice suspended when he was in the minor leagues on drug violations.
The 28-year-old asked for privacy while he is in treatment and said he planned "to speak out against impaired driving for the rest of my life, as I hope others will learn from my mistake."
Texas general manager Jon Daniels said the team commended Jeffress for seeking treatment.