The vehicle hit Animal Ark Veterinary Clinic, 3235 N. Kedzie Ave., about 6:30 p.m., officials said.
Two staff members were among those injured, said Jennifer Landini, a practice manager at the facility.
"We had to move all our animals to another facility because we have no gas, no heat," Landini said. "We're all just trying to figure out our next steps."
The driver says she hit a pothole and lost control of her car.
People who work at the clinic are concerned for their injured co- workers and the future of the clinic.
"This is our life work and to see this happen is really sad," said Landini.
She says all the animals are alright and are being taken to a sister clinic.
The Sun-Times Media Wire contributed to this report.