Woodford (shoulder) is beginning a rehab assignment Tuesday with Triple-A Memphis, Jeff Jones of the Belleville News-Democrat reports.
Woodford will work as a starter on the farm, though he's probably better suited for long relief duties considering the current state of the Cardinals' pitching depth chart. The 26-year-old right-hander posted a 5.40 ERA, 1.70 WHIP and 18:11 K:BB through 30 innings (six starts, one relief appearances) this season prior to landing on the injured list May 5 due to shoulder inflammation.