An employee at the store said the car drove into the front of the Food 4 Less on North Larkin Avenue, crashed into the self-checkout area, and eventually came to a stop in an aisle.
The car struck several people in the store, including an older customer in the self-checkout area. That older customer and the driver were taken to a local hospital for treatment.
At least one other person was treated at the scene, the source said.
The crash happened as many families were inside doing Thanksgiving dinner shopping, and as a result many of them abandoned their carts.
"I was like very shocked and my nerves got shot, I felt like numb because I was like, whoa, what the heck just happened," said witness Victor Martinez. "It almost sounded like an explosion because it barreled through the first two doors."
"It was like a bomb exploding and people were screaming and crying," said witness Cathy Duffels.
Duffels said the driver crashed through the exit doors as she and her grandson were getting ready to walk through them. She said she saw one man on the ground getting treatment and another woman screaming.
"If we would have been a little faster through that checkout line. We would have been exiting through those doors when that vehicle came rolling," she said.
"When I went to get a grocery cart there was hardly any carts left because there were so many people in the store, I'm actually surprised more people didn't get injured," Martinez said.
Crest Hill police and fire officials have not yet commented on the incident. The store is closed for the day and it was not immediately known when it would reopen.