Team officials said they considered the strain to be a minor one and that Darvish was expected to come off the DL at the earliest date possible.
Darvish will miss a scheduled start on Thursday against Baltimore and also will miss out on the All-Star Game next week. He had been named to the American League All-Star team for the second straight year.
Darvish has compiled an 8-4 record in 18 starts this season with a 3.02 earned run average.
Every pitcher who opened the season in the Texas rotation has wound up on the disabled list. Nevertheless, the Rangers went into Wednesday's game in Baltimore with the third best record in the American League.