It's not clear what caused the car to go through the Pathmark at 471 Lyons Ave. in Irvington shortly before 2 p.m.
Officials said three people were hurt, including the driver, who appeared to be ill at the time of the crash. The two other victims are believed to be workers at the supermarket.
James O'Loughlin of Irvington said he was in the parking lot getting ready to leave when he heard the crash.
"I hear a car revving up and turn to my right, and saw the car go straight into the building," he said.
"It sounded like dynamite. Like a big cracking sound, like a boom."
There have been several instances of cars crashing into supermarkets in recent months. One woman lost her leg in a November crash at Trader Joe's in Westwood, N.J., and a car plowed through another Trader Joe's on Long Island in December.
Police are investigating.