He will miss the three-game series against the Rays, and won't resume swinging a bat for at least a couple days.
Blalock may go out on a minor league rehab assignment before being activated from the disabled list.
"I haven't had a chance to discuss that with Hank," Rangers manager Ron Washington said Monday. "Right now, the only thing we're concerned about is when he can play."
Blalock originally went on the 15-day DL with a left hamstring injury on April 29, retroactive to April 26. He experienced soreness in the wrist last week.