The 8-year-old girl was conscious when she was taken to the hospital after the accident around 8:40 a.m., said Leo Flanagan, principal of the Elizabeth G. Lyons Elementary School.
The girl, whose name was not immediately released, was admitted to the pediatric intensive care unit at Boston Medical Center with serious injuries, police said.
Flanagan said the driver of the Ford Escape SUV, identified by police as 86-year-old William Geisler, had voted and was trying to exit on a school rotary. But he lost control and drove through the rotary, forcing dozens of kids to scatter.
Geisler was being treated for undisclosed injuries. He had not been charged and the investigation continued.
Counselors rushed to the school to help the children cope with having seen the accident that hurt their classmate.
"She's a beautiful, energetic, just super young kid, and hopefully whatever it is minor and her great spirit is going to get her through it," Flanagan said.
The school serves as a polling place for two precincts in Randolph, a community about 15 miles south of Boston. Town Clerk Brian Howard said voting in the presidential primary was not disrupted.