The fire started in a bedroom of a house in Fernbank Avenue.
Firefighters from Leeds and Bradford fire stations were called to the scene just after 11.15am.
Fire crews used four breathing apparatus, two hose reels and a high powered fan to clear the house of smoke.
The injured woman suffered burns to an arm and was taken to hospital by an ambulance.
A working smoke detector was fitted to the property and the fire caused the alarm to go off, the fire service said.
The cause of the fire is under investigation.