It happened at Falconbridge Animal Hospital on NC 54 at Hope Valley Road.
The accidental electrical fire broke out in the break room just before 10 p.m.
More than five appliances were plugged into a multi-plug unit in the break room.
"It is safe to say that appliances plugged into a multi-plug unit can be dangerous," said Durham Fire Chief Robert Zoldos II. "Appliances should always be plugged into an outlet by themselves, especially ones with compressors like refrigerators as they could all start up at the same time, seriously overloading the multi-plug system."
An ABC11 crew at the scene said at least 14 dogs and one reptile were rescued from the building; seven cats were killed.
The fire rekindled overnight, causing fire crews to return to the hospital and put the flames out once again.
One of the cats killed belonged to the hospital's owner, Dr. Shelli Karl.
Karl's cat, Pirate, just turned 19 last week.
"I've been wanting to do this since I was young -- since I was young. It's hard to lose. It's hard to see people lose their animals and they're so sad," Dr. Karl said.
18 employees worked at the building but Dr. Karl said they will move to her second office.
The city will assess whether the building will be condemned or not.
Dr. Karl hopes to have a memorial for the dead animals.
A GoFundMe has been started for the animal hospital. As of Thursday evening, it has raised more than $8,400 of its $10,000 goal. You can donate here.