The incident happened Sunday night behind Kean University's main campus in Union Township.
The suspect left a huge hole in the driver's side window after firing a bullet into the car.
The victim is a 27-year-old woman who lives near the school.
She is recovering from a gunshot wound to the arm.
Police Director Daniel Zieser says the woman was taken to a hospital where she was treated for non-life threatening injuries. He says she told police she was shot during an attempted carjacking and that after running away she called a campus police officer for help.
Kean University says the woman is not a student at the school. Her name was not immediately available.