The flames broke out in the kitchen of the home on Kingdom Avenue in the Huguenot section around 10:30 a.m.
At least nine cats died in the fire, but other cats and dogs survived and were being treated on the front lawn.
Firefighters were administering oxygen amid fears that more of the pets would perish. The cats that died appeared to have asphyxiated.
Officials say as many as 30 cats and seven dogs were in the house.
Six firefighters were treated for minor injuries.
The cause of the fire is under investigation.