Crystal Kelley, 46, of Princeton, was killed in the incident.
At approximately 4:44 a.m., Kelley and her 13-year-old son were involved in a crash that left her vehicle disabled in the left lane against the median.
The two climbed over the median and proceeded to walk across the northbound lanes of I-676.
Kelley was then struck by three separate vehicles as she attempted to cross, New Jersey State Police say. The driver of the second vehicle remained on scene, but the first and third continued traveling northbound.
Kelley was transported to Cooper University Hospital in Camden and pronounced dead. Her son sustained non-life-threatening injuries during the initial crash and was not injured while crossing the highway.
The first car police are looking for is described as dark in color. The third vehicle to hit Kelley is believed to be a dark-colored Nissan Maxima, year 2009-2015.
A portion of the highway was closed while police investigated.