Cueto, who compiled a 19-9 record with a 2.78 ERA in 33 regular-season starts this season, sustained the injury while facing the first batter of Saturday's Game 1 of the National League Division Series against the San Francisco Giants.
The right-hander won't be available for a Game 4 start should the best-of five NLDS extend that far -- the Reds were leading the Giants 2-games-to none heading into Tuesday's Game 3 at Cincinnati.
Cueto's availability for the rest of the series and even the remainder of the post-season was also left in doubt.
"We don't know the severity of it," Reds Manager Dusty Baker told MLB.com. "He came in [Monday] and got treatment all day long, so right now I would just be guessing to let you know how he is exactly right now. In a nutshell, we don't know."
Workers accuse National Zoo of animal mismanagement
Ohio crash that killed two caught on camera [VIDEO]