The carjacking occurred on Wednesday afternoon in the 1700 block of Las Plumas Avenue.
Police said the elderly victim had just arrived home and was at her front gate when a boy who had been standing nearby jumped inside her car and locked its doors.
The victim saw the suspect and tried to stop him by banging on the windows, but the boy started the car and drove off, knocking the victim down, according to police.
When officers arrived, she was being treated at the scene and then was transported to a hospital where she underwent surgery for broken bones, a dislocated shoulder and multiple lacerations, according to police.
She is recovering from her injuries but remained in the hospital today.
The boy was arrested at about 9:20 a.m. Monday in the 100 block of Rosebay Court.
Officers, who had responded to a report of a suspicious vehicle, saw a juvenile climbing fences and, a short time later, detained him without incident.
Anyone with information about the case is asked to call Detective Brian McDonald at (408) 277-4166 or to remain anonymous, call Silicon Valley Crime Stoppers at (408) 947-STOP (7867) or visit http://svcrimestoppers.org.