Crews from Killingbeck and Moortown were sent to Naburn Fold in Whinmoor shortly before 3pm today.
They used four sets of breathing apparatus and a hose reel while putting out the fire.
A West Yorkshire Fire Service spokesman said firefighters had rescued one 'male casualty' from inside the property.
He said an ambulance was also requested for two more people suffering from smoke inhalation.
A fire investigation officer is now looking into the cause of the fire.