The crash happened in Montvale, Bergen County, near the James Gandolfini Service Area at mile marker 170.9, officials said.
Montvale Mayor Mike Ghassali said the school bus was heading to New York State when it overturned just south of Exit 172 around 7:30 p.m.
In a post on Facebook, the mayor said no fatalities have been reported, and the most serious injury "now has a pulse."
Of the 31 total occupants, Ghassali said 13 were taken to local hospitals.
According to New Jersey Governor Phil Murphy, the school bus is from Lakewood.
He said New Jersey State Police and the Department of Transportation are on the scene.
Further details on the crash were not immediately available.