The accident happened at KD Learning Center, in a shopping center on Uvalde at Wallisville.
According to the Harris County Sheriff's Office, an 81-year-old woman was picking up her grandchild and a family friend's four-year-old son from the day care. She put the vehicle in reverse to leave, thinking the children were in the car, but the four-year-old was still trying to get in. He was struck by the open door, and pushed under the vehicle.
When the driver got out to try to help the boy, authorities say she didn't put the vehicle in park. The car rolled backwards, sideswiped another vehicle and slammed into the day care.
"She called me and said a vehicle went into the vehicle and he was the only one hit," family friend Sheila Johnson said.
The children inside the day care were in a back area, and no one in the building was injured.
Bystanders performed CPR and the child was taken to a hospital by Life Flight, but he died of head trauma.
"My heart goes out to the family," Johnson said.
Officials say the day care will remain closed for now.