The incident happened around 2 a.m. on the 300 block of West California Boulevard.
Authorities said it appears the woman dropped a cigarette on her couch, causing the fire.
The 70-year-old victim was pronounced dead at the scene. Her cat suffered critical injuries and later died as it was being transferred to a local animal shelter.
Authorities said the fire was contained to one room, and it took crews 10 minutes to extinguish the flames.
Firefighters said there were no smoke detectors in the woman's home, but smoke detectors in the hallways of the building alerted other residents.