Hawpe, who signed a Minor League deal with the Rangers in January and is in camp as a non-roster invitee, was expected to lead off every inning of the contest in his first action of Spring Training.
"I just overdid it," Hawpe said of his Wednesday workout, which caused the setback. "I doubled up on some infield and doubled up on some outfield, and then after hitting, I felt it during conditioning."
The 32-year-old veteran has spent eight years in the big leagues, but is with his fourth club since 2010. He spent most of the first seven years of his career with the Rockies, where he was an All-Star in '09.
Hawpe said he'll rest the hamstring on Thursday before resuming workouts on Friday, though he didn't know what that would entail.
"Just give it a day," Hawpe said. "Get back at it tomorrow."