In a corresponding move, the Cardinals recalled catcher Michael McKenry from Triple-A Memphis.
Carpenter left Wednesday night's game against the Pittsburgh Pirates in the third inning with the injury.
Carpenter clutched his right side and shook his head after trying to check a swing on a 3-and-1 pitch from Jeff Locke. He was examined briefly on the field by a medical trainer before walking off with the trainer and manager Mike Matheny.
Matheny said an MRI showed a Grade 2 strain in Carpenter's oblique. He did not offer a timetable for his return.
A three-time All-Star, Carpenter leads the National League with a .991 OPS. He had a similar injury in 2012 and missed a month of action with a strained right side.
The Cardinals' infield is becoming rapidly depleted. Third baseman Jhonny Peralta left Tuesday's game and was unavailable to play Wednesday because of discomfort in the same thumb he had surgery on in March. The Cardinals hope Peralta can return to play Thursday or Friday.
Additionally, first baseman/outfielder Brandon Moss went on the disabled list Tuesday with a sprained ankle.
The team also put backup catcher Brayan Peña on the DL before Wednesday's game because of inflammation in his surgically repaired left knee.
ESPN's Mark Saxon contributed to this report