Toye R. Norris, 40, of Wilmington, is being sought by investigators for the Sunday morning incident.
According to authorities, Norris went to the Food Lion store at 3609 Philadelphia Pike in Claymont with a small child.
She then allegedly filled a cart with $100 worth of diapers and left the store without paying.
An employee confronted Norris in the parking lot, police said, but she continued to a grey Volvo station wagon.
Police say Norris put the diapers in the car, then placed the child in the car without securing him.
As she drove out of the parking lot, police say the door adjacent to where the child had been placed was left open.
The identity of the child is unknown, police say. It is also unknown if the child was hurt.
State police have obtained warrants on Norris charging her with one count each of Shoplifting, Endangering the Welfare of a Child, Driving While Suspended, Reckless Driving, Having Expired Registration, and Failure to Secure a Child in a Child Restraint.