The incident happened at Lillian's Grocery Store at Main and Westland streets around 3:20 a.m.
Police said while the front of the SUV is damaged, no one was inside when they got on scene. The SUV also had no license plate, but is described as a dark blue Chevy.
Police are finishing up their inspection, and the Hartford Fire Department was called to the scene too.
Police are looking for the occupants of the SUV.
The owner of the store's son said that he looked over the surveillance footage and saw that the car crashed into the building four times. He says they've been in the neighborhood for 7 years and have experienced break-ins before.
Police said the SUV was stolen from a nearby car dealership.
No injuries were reported.