It happened around 12:15 a.m. Sunday at the Brandywine Valley SPCA in New Castle County.
The family identifies the driver as a 33-year-old Latoya Cooper, a mother of five.
Juanetta Cooper, Latoya's mother, said she got a call from authorities soon after the crash.
"She went through the stop sign and must have kept going through. I just was bawling," Juanetta Cooper said.
Officials said the driver lost control of her vehicle and crashed into the building; the impact of the crash resulted in a fire.
Emergency personnel and volunteers removed 100 animals from the burning building.
Two cats needed emergency veterinary care; one died from its injuries, and the other is being treated for burns and smoke inhalation. Two other cats lost their lives in the fire. The other animals have been relocated to temporary housing and are being examined by medical personnel.
A total of 98 animals, 36 cats and 62 dogs, were moved to other locations.
The fire was extinguished within a half hour, but it severely damaged the veterinary clinic inside the structure.
Smoke and water also caused damage to the shelter section of the building.
SPCA officials say they are incredibly thankful for the rapid response from firefighters and neighbors who saved the surviving animals.
The facility will be closed for an undetermined period of time, pending a building inspection and possible subsequent cleanup and repairs.
This same SPCA branch recently agreed to take on animals from lower Delaware while the facility there expands.
Police have not yet determined what caused the driver to crash into the building.
The BVSPCA said financial donations are needed to help with the additional cost to care for the animals and the damage to the building.