Police said the driver of a black Ford pickup truck pulled alongside Sabra Leavy as she walked to her car at the Walmart on Forest Lane in North Dallas.
"You could actually see the truck roll over her like she was a speed bump," witness Dominique Duncan said.
She and a friend, Kimberly Butler, were walking into Walmart at the time of the incident.
"They were laughing about it after they snatched her purse and they ran her over," Butler said. "They were laughing as they drove off. It was horrible."
Linda Hazouri, Leavy's daughter, said the weight of the approximately 8,000-pound truck ruptured her mother's bladder and shattered her pelvis.
"We don't know if she's going to be able to walk or anything at this point," she said.
Leavy, who is in intensive care at Parkland, is scheduled for surgery Friday morning.
Investigators said they believe the driver lured Leavy over to his car window by pretending to apologize to her.
"The driver began saying, 'I'm sorry I parked so close to your car,'" Senior Cpl. Kevin Janse said. "When she did get closer to his window, he reached out while still in drive and grabbed her purse where she couldn't let go."
The man dragged Leavy across the parking lot until she was able to break free. The driver then ran over her, police said.
"She just kept saying she was hurting and they stole her purse, and she asked me to hold her, and I did," Butler said. "I laid on the ground and covered her up with my body, until they brung her with a blanket."
Police said there is surveillance video of the crime but have not yet released it.
"Hopefully we can find this person that did this to such an innocent person, a person that did no harm to no one," Hazouri said. "She was just out shopping for groceries."
A spokesperson for Walmart said the store is appalled by what happened and is working closely with police to see that there is an arrest in the case.