The pedestrians were injured just after 6:20 p.m. local time, Chicago police and fire officials said.
One of the pedestrians held onto the car as it fled the scene before the vehicle was stopped by an ambulance on the nearby Dan Ryan Expressway, officials said. The person clinging to the car and one of the three outside the stadium were in critical condition. The other two pedestrians were in serious condition, officials said.
According to the White Sox, the injured were treated at the scene and transported to area hospitals.
In addition, the driver of the vehicle and three others in the car were hospitalized with various injuries. Illinois State Police and Chicago Police apprehended the suspect blocks away from where the hit and run took place.
According to Fred Melean, the deputy chief of the Chicago Police Department, all four in the vehicle were in custody at the hospital.
"Our hearts go out to the four fans who were injured this evening, their families and friends, as well as the fans who witnessed the incident on their way to a baseball game," the team said. "The Chicago White Sox organization expresses its appreciation to the Chicago Police Department, the Chicago Fire Department, the Illinois State Police and others, including fans, who responded to the incident and provided immediate care for the victims."
Information from The Associated Press was used in this report.