Two fire engines from Leyland and Bamber Bridge were sent to the incident at Spring Gardens in the town at 2.20pm
One person was treated for suspected smoke inhalation by firefighters at the scene before being taken to hospital.
A spokesman for Lancashire Fire and Rescue Service (LFRS) said: "The fire was in the front bedroom of a domestic upstairs flat and firefighters used two breathing apparatus, one hose reel and a positive ventilation fan to extinguish the fire.
"Firefighters were at the scene for approximately fifty minutes."
LFRS was contacted for further comment.