Stephenson, 25, suffered the injury when he was hit by the foul tip from Cardinals first baseman Paul Goldschmidt in the first inning. Stephenson left the game after being unable to make a throw on Goldschmidt's chopper between the plate and mound.
"I thought the pain would go away, but when I went to throw, I couldn't do it," Stephenson said. "I have to sleep in a chair. I can feel the bones rub together. The good thing is no surgery. It just has to heal right."
The Reds placed Stephenson on the 10-day injured list Saturday and called up catcher Mark Kolozsvary from Triple-A Louisville.
This is a third notable injury for Stephenson this season. He also suffered a concussion in April and a fractured right thumb in June.
He is hitting .319 with six home runs and 35 RBIs in 50 games this season.
Kolozsvary, 26, is 1-for-11 with an RBI in seven games for the Reds in 2022.
The Associated Press contributed to this report.