Brinkley, 23, was shot multiple times early Friday morning as his car was stopped at an intersection in Cheltenham, police said. Investigators are looking for a gunman who fled the scene in a car. They did not have a motive.
Brinkley was able to drive himself a short distance, then was taken to a hospital by a police officer who responded to the shooting, according to Cheltenham Township police.
He was listed in stable condition at Albert Einstein Medical Center in Philadelphia, hospital spokesman Rodney Yancey said.
In a statement, the Chargers wished Brinkley a speedy recovery but said they would have no further comment while the shooting was under investigation.
It is the third time in six years a Chargers player has been shot. In September 2006, linebacker Steve Foley was shot three times by an off-duty police officer in Coronado, Calif., who suspected him of driving drunk. The injury ended his career.
In July 2003, rookie safety Terrence Kiel was shot during an attempted carjacking in Houston. Four years later, he pleaded guilty to felony and misdemeanor drug charges for shipping prescription cough syrup to Texas. He was released by the team after his plea and died in a car crash in July 2008.
Brinkley signed with the Chargers as a rookie free agent following this year's draft. As a senior at Syracuse last season, he rushed for 1,164 yards and seven touchdowns.
A native of Philadelphia, Brinkley was a prolific running back at West Catholic High School. He set city high school records with 7,429 career rushing yards and 85 touchdowns.
In a statement, Syracuse coach Doug Marrone extended the program's thoughts and prayers to Brinkley and his family, wishing him a speedy recovery.
Information from The Associated Press was used in this report.