It happened at about 10:30 a.m. at the restaurant at 680 Somerset Street.
Police say a Range Rover drifted out of its lane on Somerset Street and hit a Toyota Camry, causing the Range Rover to lose control and go through the front of the building.
The driver of the Range Rover, 40-year old Fatmata Kamara of Monmouth Junction, and her passengers, two boys ages 10 and 11, were taken to Robert Wood Johnson University Hospital with non-life threatening injuries.
Police say no customers or workers were injured in the restaurant.
Kamara was issued a summons for careless driving.
The White Castle has been shut down for repairs.