Carpenter, 37, will stay in the Dallas area for the next few days to recover before returning to St. Louis to begin his rehab.
With an expected rehabilitation time of two to three months, Carpenter should have a normal offseason and be ready come the start of the 2013 season.
"We are pleased with today's results, and Chris will soon return to St. Louis to begin his rehab," Cardinals general manager John Mozeliak said. "We look forward to seeing Chris around the ballpark during his recovery."
Quinn Roberts is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.