The driver of the car has been detained, police said, adding that there was no further danger posed to the public, Reuters reported.
"There are currently no indications of an attack or an intentional act," Stuttgart police said on X.
The incident, which occurred shortly before 6 p.m. (1600 GMT), took place near the Olgaeck tram station.
The Bild newspaper cited eyewitnesses as saying a woman with a pram had been hit by the black Mercedes G-Class SUV.
The area of the incident was blocked off by police, who advised pedestrians and drivers to avoid the area if possible.